Geometry Complete Unit 3 - highschoolmathteachers.com · Unit 3 Pacing Chart...
Transcript of Geometry Complete Unit 3 - highschoolmathteachers.com · Unit 3 Pacing Chart...
Complete Unit 3
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HighSchoolMathTeachers.com©2020
Table of Contents
Unit 3 Pacing Chart -------------------------------------------------------------------------------------------- 1
Geometry Unit 3 Skills List ---------------------------------------------------------------------------------------- 5
Unit 3 Lesson Plans -------------------------------------------------------------------------------------------- 6
Day 31 Bellringer -------------------------------------------------------------------------------------------- 33
Day 31 Activity -------------------------------------------------------------------------------------------- 36
Day 31 Practice -------------------------------------------------------------------------------------------- 39
Day 31 Exit Slip -------------------------------------------------------------------------------------------- 44
Day 32 Bellringer -------------------------------------------------------------------------------------------- 46
Day 32 Activity -------------------------------------------------------------------------------------------- 48
Day 32 Practice -------------------------------------------------------------------------------------------- 51
Day 32 Exit Slip -------------------------------------------------------------------------------------------- 55
Day 33 Bellringer -------------------------------------------------------------------------------------------- 57
Day 33 Activity -------------------------------------------------------------------------------------------- 59
Day 33 Practice -------------------------------------------------------------------------------------------- 62
Day 33 Exit Slip -------------------------------------------------------------------------------------------- 66
Day 34 Bellringer -------------------------------------------------------------------------------------------- 68
Day 34 Activity -------------------------------------------------------------------------------------------- 70
Day 34 Practice -------------------------------------------------------------------------------------------- 72
Day 34 Exit Slip -------------------------------------------------------------------------------------------- 76
Week 7 Assessment -------------------------------------------------------------------------------------------- 78
Day 36 Bellringer -------------------------------------------------------------------------------------------- 87
Day 36 Activity -------------------------------------------------------------------------------------------- 89
Day 36 Practice -------------------------------------------------------------------------------------------- 91
Day 36 Exit Slip -------------------------------------------------------------------------------------------- 109
Day 37 Bellringer -------------------------------------------------------------------------------------------- 111
Day 37 Activity -------------------------------------------------------------------------------------------- 113
Day 37 Practice -------------------------------------------------------------------------------------------- 116
Day 37 Exit Slip -------------------------------------------------------------------------------------------- 127
Day 38 Bellringer -------------------------------------------------------------------------------------------- 129
Day 38 Activity -------------------------------------------------------------------------------------------- 132
Day 38 Practice -------------------------------------------------------------------------------------------- 134
Day 38 Exit Slip -------------------------------------------------------------------------------------------- 149
Day 39 Bellringer -------------------------------------------------------------------------------------------- 151
Day 39 Activity -------------------------------------------------------------------------------------------- 155
Day 39 Practice -------------------------------------------------------------------------------------------- 157
Day 39 Exit Slip -------------------------------------------------------------------------------------------- 171
Week 8 Assessment -------------------------------------------------------------------------------------------- 173
Day 41 Bellringer -------------------------------------------------------------------------------------------- 182
Day 41 Activity -------------------------------------------------------------------------------------------- 187
Day 41 Practice -------------------------------------------------------------------------------------------- 190
Day 41 Exit Slip -------------------------------------------------------------------------------------------- 210
Day 42 Bellringer -------------------------------------------------------------------------------------------- 213
Day 42 Activity -------------------------------------------------------------------------------------------- 215
Day 42 Practice -------------------------------------------------------------------------------------------- 217
Day 42 Exit Slip -------------------------------------------------------------------------------------------- 227
Day 43 Bellringer -------------------------------------------------------------------------------------------- 229
Day 43 Activity -------------------------------------------------------------------------------------------- 231
Day 43 Practice -------------------------------------------------------------------------------------------- 234
Day 43 Exit Slip -------------------------------------------------------------------------------------------- 255
Day 44 Bellringer -------------------------------------------------------------------------------------------- 257
Day 44 Activity -------------------------------------------------------------------------------------------- 261
Day 44 Practice -------------------------------------------------------------------------------------------- 263
Day 44 Exit Slip -------------------------------------------------------------------------------------------- 281
Week 9 Assessment -------------------------------------------------------------------------------------------- 283
Unit 3 Test -------------------------------------------------------------------------------------------- 290
Unit 3 Pacing Chart
HighSchoolMathTeachers.com ©2020 Page 1
Unit Week Day CCSS Standards Objective I Can Statements
Unit 3 Triangles
Week 7 – Prove Theorems
about Triangles 31
CCSS.MATH.CONTENT.HSG.CO.C.10 Prove theorems about triangles. Theorems include:
measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the
segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the
medians of a triangle meet at a point.
Prove that measures of interior angles of a triangle
sum to 180°
I can prove that measures of interior angles of a triangle sum
to 180°
Unit 3 Triangles
Week 7 – Prove Theorems
about Triangles 32
CCSS.MATH.CONTENT.HSG.CO.C.10 Prove theorems about triangles. Theorems include:
measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the
segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the
medians of a triangle meet at a point.
Prove that base angles of isosceles triangles are
congruent
I can prove that base angles of isosceles triangles are congruent
Unit 3 Triangles
Week 7 – Prove Theorems
about Triangles 33
CCSS.MATH.CONTENT.HSG.CO.C.10 Prove theorems about triangles. Theorems include:
measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the
segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the
medians of a triangle meet at a point.
Prove that the medians of a triangle meet at a point.
I can prove that the medians of a triangle meet at a point.
Unit 3 Triangles
Week 7 – Prove Theorems
about Triangles 34
CCSS.MATH.CONTENT.HSG.CO.C.10 Prove theorems about triangles. Theorems include:
measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the
segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the
medians of a triangle meet at a point.
Summarize the week's topics
I can prove that measures of interior angles of a triangle sum
to 180° I can prove that base angles of
isosceles triangles are congruent I can prove that the medians of a
triangle meet at a point.
Unit 3 Pacing Chart
HighSchoolMathTeachers.com ©2020 Page 2
Unit 3 Triangles
Week 7 – Prove Theorems
about Triangles 35 Assessment Assessment Assessment
Unit 3 Triangles
Week 8 – Geometric
Constructions 36
CCSS.MATH.CONTENT.HSG.CO.D.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric
software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing
perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line
parallel to a given line through a point not on the line.
Make formal geometric constructions with a variety
of tools and methods (compass and straightedge,
string, reflective devices, paper folding, dynamic
geometric software, etc.). Copying a segment;
copying an angle; bisecting a segment; bisecting an
angle;
I can copy a segment; an angle; bisecting a segment and bisecting
an angle using variety of tools and methods (compass and
straightedge, string, reflective devices, paper folding, dynamic
geometric software, etc.)
Unit 3 Triangles
Week 8 – Geometric
Constructions 37
CCSS.MATH.CONTENT.HSG.CO.D.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric
software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing
perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line
parallel to a given line through a point not on the line.
Make formal geometric constructions with a variety
of tools and methods (compass and straightedge,
string, reflective devices, paper folding, dynamic
geometric software, etc.).constructing
perpendicular lines, including the perpendicular bisector of a line segment
I can construct perpendicular
lines, including the perpendicular bisector of a line segment using
variety of tools and methods (compass and straightedge,
string, reflective devices, paper folding, dynamic geometric
software, etc.)
Unit 3 Pacing Chart
HighSchoolMathTeachers.com ©2020 Page 3
Unit 3 Triangles
Week 8 – Geometric
Constructions 38
CCSS.MATH.CONTENT.HSG.CO.D.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric
software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing
perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line
parallel to a given line through a point not on the line.
Make formal geometric
constructions with a variety of tools and methods
(compass and straightedge, string, reflective devices, paper folding, dynamic
geometric software, etc.). constructing a line parallel to a given line through a
point not on the line.
I can construct a line parallel to a given line through a point not on the line uisng variety of tools and
methods (compass and straightedge, string, reflective
devices, paper folding, dynamic geometric software, etc.)
Unit 3 Triangles
Week 8 – Geometric
Constructions 39
CCSS.MATH.CONTENT.HSG.CO.D.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric
software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing
perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line
parallel to a given line through a point not on the line.
Summarize- Copying a segment; copying an angle;
bisecting a segment; bisecting an angle;
constructing perpendicular lines, including the
perpendicular bisector of a line segment; and
constructing a line parallel to a given line through a
point not on the line.
I can copy a line segment; an angle; bisect a segment and an
angle I can constructing perpendicular lines, including the perpendicular
bisector of a line segment I can constructing a line parallel to a given line through a point
not on the line.
Unit 3 Triangles
Week 8 – Geometric
Constructions 40 Assessment Assessment Assessment
Unit 3 Pacing Chart
HighSchoolMathTeachers.com ©2020 Page 4
Unit 3 Triangles
Week 9 – Inscribed and Circumscribed
Circles of a Triangle
41 CCSS.MATH.CONTENT.HSG.CO.D.13
Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
Construct an equilateral triangle inscribed in a
circle.
I can construct an equilateral triangle inscribed in a circle.
Unit 3 Triangles
Week 9 – Inscribed and Circumscribed
Circles of a Triangle
42 CCSS.MATH.CONTENT.HSG.CO.D.13
Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
Construct an square inscribed in a circle.
I can construct an square inscribed in a circle.
Unit 3 Triangles
Week 9 – Inscribed and Circumscribed
Circles of a Triangle
43 CCSS.MATH.CONTENT.HSG.CO.D.13
Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
Construct a regular hexagon inscribed in a
circle.
I can construct a regular hexagon inscribed in a circle.
Unit 3 Triangles
Week 9 – Inscribed and Circumscribed
Circles of a Triangle
44 CCSS.MATH.CONTENT.HSG.CO.D.13
Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
Sammarize - Construction of a equilateral triangle, a
square, and a regular hexagon inscribed in a
circle
I can construct an equilateral triangle inscribed in a circle.
I can construct an square inscribed in a circle.
I can construct a regular hexagon inscribed in a circle.
Unit 3 Triangles
Week 9 – Inscribed and Circumscribed
Circles of a Triangle
45 Assessment Assessment Assessment
Geometry Unit 3 Skills List Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 5
Geometry Unit 3 Skills List
Number Unit CCSS Skill
12 3 HSG.CO.C.10 Prove theorems about triangles
13 3 HSG.CO.D.12 Make formal geometric constructions
14 3 HSG.CO.D.13 Construct inscribed figures
Geometry Unit 3 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 6
Unit: Unit 3 Triangles
Course: Geometry
Topic: Week 7 – Prove Theorems about Triangles
Day: 31
Common Core State Standard: CCSS.MATH.CONTENT.HSG.CO.C.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
Mathematical Practice: CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically.
Objective: Prove that measures of interior angles of a triangle sum to 180°
I can statement: I can prove that measures of interior angles of a triangle sum to 180°
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 4. Students will discover that when the interior angles of a triangle are summed up, they add up to 180°. 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Materials: Bellringer 31 Day 31 Activities Day 31 Practice Day 31 Presentation Day 31 Exit Slip
Geometry Unit 3 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 7
Accommodations/Special Circumstances:
Technology:
Reflection:
Extra/Additional Resources:
Geometry Unit 3 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 8
Unit: Unit 3 Triangles
Course: Geometry
Topic: Week 7 – Prove Theorems about Triangles
Day: 32
Common Core State Standard: CCSS.MATH.CONTENT.HSG.CO.C.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
Mathematical Practice: CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically.
Objective: Prove that base angles of isosceles triangles are congruent
I can statement: I can prove that base angles of isosceles triangles are congruent
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 4. Students will discover that an isosceles triangle has at least two equal sides and consequently its base angles are congruent through simple paper folding and cutting 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Materials: Bellringer 32 Day 32 Activities Day 32 Practice Day 32 Presentation Day 32 Exit Slip
Geometry Unit 3 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 9
Accommodations/Special Circumstances:
Technology:
Reflection:
Extra/Additional Resources:
Geometry Unit 3 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 10
Unit: Unit 3 Triangles
Course: Geometry
Topic: Week 7 – Prove Theorems about Triangles
Day: 33
Common Core State Standard: CCSS.MATH.CONTENT.HSG.CO.C.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
Mathematical Practice: CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically.
Objective: Prove that the medians of a triangle meet at a point.
I can statement: I can prove that the medians of a triangle meet at a point.
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3. Students are required to draw an equilateral triangle and its medians to study where and how they meet. 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Materials: Bellringer 33 Day 33 Activities Day 33 Practice Day 33 Presentation Day 33 Exit Slip
Geometry Unit 3 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 11
Accommodations/Special Circumstances:
Technology:
Reflection:
Extra/Additional Resources:
Geometry Unit 3 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 12
Unit: Unit 3 Triangles
Course: Geometry
Topic: Week 7 – Prove Theorems about Triangles
Day: 34
Common Core State Standard: CCSS.MATH.CONTENT.HSG.CO.C.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
Mathematical Practice: CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others.
Objective: Summarize the week's topics
I can statement: I can prove that measures of interior angles of a triangle sum to 180° I can prove that base angles of isosceles triangles are congruent I can prove that the medians of a triangle meet at a point.
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 5. Students are required to draw an Isosceles triangle then prove that the base angles are equal equal, the sum of interior angles is 180° and the medians intersect at a common point.
Materials: Bellringer 34 Day 34 Activities Day 34 Practice Day 34 Presentation Day 34 Exit Slip
Geometry Unit 3 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 13
3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day. Accommodations/Special Circumstances:
Technology:
Reflection:
Extra/Additional Resources:
Geometry Unit 3 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 14
Unit: Unit 3 Triangles
Course: Geometry
Topic: Week 7 – Prove Theorems about Triangles
Day: 35
Common Core State Standard: Assessment
Mathematical Practice: Assessment
Objective: Assessment
I can statement: Assessment
Procedures: Assessment
Materials: Assessment
Accommodations/Special Circumstances:
Technology:
Reflection:
Extra/Additional Resources:
Geometry Unit 3 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 15
Unit: Unit 3 Triangles
Course: Geometry
Topic: Week 8 – Geometric Constructions
Day: 36
Common Core State Standard: CCSS.MATH.CONTENT.HSG.CO.D.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
Mathematical Practice: CCSS.MATH.PRACTICE.MP4 Model with mathematics.
Objective: Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle;
I can statement: I can copy a segment; an angle; bisecting a segment and bisecting an angle using variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.)
Geometry Unit 3 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 16
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of four to copy a line segment using a straightedge, a ruler, a pencil, a pair of compasses and an A4 size plain paper. 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Materials: Bellringer 36 Day 36 Activities Day 36 Practice Day 36 Presentation Day 36 Exit Slip
Accommodations/Special Circumstances:
Technology:
Reflection:
Extra/Additional Resources:
Geometry Unit 3 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 17
Unit: Unit 3 Triangles
Course: Geometry
Topic: Week 8 – Geometric Constructions
Day: 37
Common Core State Standard: CCSS.MATH.CONTENT.HSG.CO.D.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
Mathematical Practice: CCSS.MATH.PRACTICE.MP4 Model with mathematics.
Objective: Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).constructing perpendicular lines, including the perpendicular bisector of a line segment
I can statement: I can construct perpendicular lines, including the perpendicular bisector of a line segment using variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.)
Geometry Unit 3 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 18
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 4. Students are required to draw perpendicular lines using a string 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Materials: Bellringer 37 Day 37 Activities Day 37 Practice Day 37 Presentation Day 37 Exit Slip
Accommodations/Special Circumstances:
Technology:
Reflection:
Extra/Additional Resources:
Geometry Unit 3 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 19
Unit: Unit 3 Triangles
Course: Geometry
Topic: Week 8 – Geometric Constructions
Day: 38
Common Core State Standard: CCSS.MATH.CONTENT.HSG.CO.D.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
Mathematical Practice: CCSS.MATH.PRACTICE.MP4 Model with mathematics.
Objective: Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). constructing a line parallel to a given line through a point not on the line.
I can statement: I can construct a line parallel to a given line through a point not on the line uisng variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.)
Geometry Unit 3 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 20
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 4. we would like construct parallel lines using a paper folding technique. 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Materials: Bellringer 38 Day 38 Activities Day 38 Practice Day 38 Presentation Day 38 Exit Slip
Accommodations/Special Circumstances:
Technology:
Reflection:
Extra/Additional Resources:
Geometry Unit 3 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 21
Unit: Unit 3 Triangles
Course: Geometry
Topic: Week 8 – Geometric Constructions
Day: 39
Common Core State Standard: CCSS.MATH.CONTENT.HSG.CO.D.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
Mathematical Practice: CCSS.MATH.PRACTICE.MP8 Look for and express regularity in repeated reasoning.
Objective: Summarize- Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
I can statement: I can copy a line segment; an angle; bisect a segment and an angle I can constructing perpendicular lines, including the perpendicular bisector of a line segment I can constructing a line parallel to a given line through a point not on the line.
Geometry Unit 3 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 22
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3. Students are required to construct a perpendicular lines through paper folding. 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Materials: Bellringer 39 Day 39 Activities Day 39 Practice Day 39 Presentation Day 39 Exit Slip
Accommodations/Special Circumstances:
Technology:
Reflection:
Extra/Additional Resources:
Geometry Unit 3 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 23
Unit: Unit 3 Triangles
Course: Geometry
Topic: Week 8 – Geometric Constructions
Day: 40
Common Core State Standard: Assessment
Mathematical Practice: Assessment
Objective: Assessment
I can statement: Assessment
Procedures: Assessment
Materials: Assessment
Accommodations/Special Circumstances:
Technology:
Reflection:
Extra/Additional Resources:
Geometry Unit 3 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 24
Unit: Unit 3 Triangles
Course: Geometry
Topic: Week 9 – Inscribed and Circumscribed Circles of a Triangle
Day: 41
Common Core State Standard: CCSS.MATH.CONTENT.HSG.CO.D.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
Mathematical Practice: CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically.
Objective: Construct an equilateral triangle inscribed in a circle.
I can statement: I can construct an equilateral triangle inscribed in a circle.
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 4. They will draw an equilateral triangle inscribed in a circle using a straightedge and a pair of compasses. 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Materials: Bellringer 41 Day 41 Activities Day 41 Practice Day 41 Presentation Day 41 Exit Slip
Accommodations/Special Circumstances:
Technology:
Geometry Unit 3 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 25
Reflection:
Extra/Additional Resources:
Geometry Unit 3 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 26
Unit: Unit 3 Triangles
Course: Geometry
Topic: Week 9 – Inscribed and Circumscribed Circles of a Triangle
Day: 42
Common Core State Standard: CCSS.MATH.CONTENT.HSG.CO.D.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
Mathematical Practice: CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically.
Objective: Construct an square inscribed in a circle.
I can statement: I can construct an square inscribed in a circle.
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3. we would construct a square inside a circle using a pairs of compass and a straightedge. 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Materials: Bellringer 42 Day 42 Activities Day 42 Practice Day 42 Presentation Day 42 Exit Slip
Accommodations/Special Circumstances:
Technology:
Geometry Unit 3 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 27
Reflection:
Extra/Additional Resources:
Geometry Unit 3 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 28
Unit: Unit 3 Triangles
Course: Geometry
Topic: Week 9 – Inscribed and Circumscribed Circles of a Triangle
Day: 43
Common Core State Standard: CCSS.MATH.CONTENT.HSG.CO.D.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
Mathematical Practice: CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically.
Objective: Construct a regular hexagon inscribed in a circle.
I can statement: I can construct a regular hexagon inscribed in a circle.
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least three to construct a regular polygon inscribed in a circle using paper folding 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Materials: Bellringer 43 Day 43 Activities Day 43 Practice Day 43 Presentation Day 43 Exit Slip
Accommodations/Special Circumstances:
Technology:
Geometry Unit 3 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 29
Reflection:
Extra/Additional Resources:
Geometry Unit 3 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 30
Unit: Unit 3 Triangles
Course: Geometry
Topic: Week 9 – Inscribed and Circumscribed Circles of a Triangle
Day: 44
Common Core State Standard: CCSS.MATH.CONTENT.HSG.CO.D.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
Mathematical Practice: CCSS.MATH.PRACTICE.MP4 Model with mathematics.
Objective: Summarize - Construction of a equilateral triangle, a square, and a regular hexagon inscribed in a circle
I can statement: I can construct an equilateral triangle inscribed in a circle. I can construct an square inscribed in a circle. I can construct a regular hexagon inscribed in a circle.
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3. They will construct a square inscribed in a circle 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Materials: Bellringer 44 Day 44 Activities Day 44 Practice Day 44 Presentation Day 44 Exit Slip
Accommodations/Special Circumstances:
Technology:
Geometry Unit 3 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 31
Reflection:
Extra/Additional Resources:
Geometry Unit 3 Lesson Plan Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 32
Unit: Unit 3 Triangles
Course: Geometry
Topic: Week 9 – Inscribed and Circumscribed Circles of a Triangle
Day: 45
Common Core State Standard: Assessment
Mathematical Practice: Assessment
Objective: Assessment
I can statement: Assessment
Procedures: Assessment
Materials: Assessment
Accommodations/Special Circumstances:
Technology:
Reflection:
Extra/Additional Resources:
Day 31 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 33
1. In the figure below lines PQ and RS are parallel. State whether the following angles are corresponding,
alternate interior or alternate exterior angles.
(a) ∠2 and ∠7
(b) ∠3 and ∠7
(c) ∠3 and ∠6
1 2
3 4
5 6
7 8
P
Q
R
S
Day 31 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 34
2. Find the alternate interior and alternate exterior angles represented by letters. The two lines shown
in each case are parallel.
(a)
(b)
113°
𝑥 𝑦
31°
𝑥 𝑦
Day 31 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 35
Answer Keys
Day 31:
1. (a) Alternate interior angles
(b) Corresponding angles
(c) Alternate exterior angles
2. (a) 𝑥 = 113°, 𝑦 = 67°
(b) 𝑥 = 31°, 𝑦 = 149°
Day 31 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 36
1. On the plain paper provided, draw two straight lines of about 5 inches each on either sides of the
ruler to form a pair of parallel lines as shown below. Label the two lines as PQ and RS as shown below.
2. Mark a point, A, on line PQ at the position shown below.
3. Similarly, mark two points, B and C on line RS in the positions shown below.
4. Now, using a ruler draw two lines, from point A to point C and from point A to point B respectively as
shown below.
P Q
R S
A P Q
R S
A
B C
P Q
R S
A
B C
P Q
R S
Day 31 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 37
5. What name is given to the plane figure formed between points A, B and C?
6. Consider the following angles: ∠BAC, ∠ABC and ∠ACB. Are these angles located within or outside the
plane figure you have identified in 5 above?
7. Measure these three angles accurately using a protractor: ∠BAC, ∠ABC and ∠ACB and write down
their measures.
8. What is the sum of these three angles? Do you think this is usually the case for any plane figure of the
same kind?
Day 31 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 38
In this activity students will work in groups of four to discover that when the interior angles of a triangle
are summed up, they add up to 180°. Students in the respective groups will require a pencil, a plain
paper, a ruler and a protractor. It is assumed from the foregoing that students are comfortable with
measuring angles using a protractor.
Answer Keys
Day 31:
1. No response
2. No response
3. No response
4. No response
5. Triangle
6. Located within the plane figure
7. Each of the three angles will vary from group to group depending on the triangle they have come up
with.
8. The sum should be accurately 180°. This is a question to enable the students think of any other
triangle having interior angles summing up to 180° though most of them will agree.
Day 31 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 39
Use the figure below to answer question 1-5. RS ∥ PQ and the two transversal lines intersect the pair of
parallel lines to form triangle ABC as shown below.
1. Find the measure of ∠𝑦
2. Find the measure of ∠𝑧
3. Find the measure of ∠𝑥
4. Find the sum of ∠𝑥, ∠𝑦 and ∠𝑧.
5. What is your conclusion about the sum in question 4 in relation to the triangle formed above?
x
z y
A
P Q
R S
B C 44°
59°
Day 31 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 40
Use the figure below to answer questions 6-13. Triangle PQR is formed between the parallel lines.
6. Find the measure of ∠𝑦
7. Find the measure of ∠CQP
8. Find the measure of ∠BPQ
9. Find the measure of ∠BPR
10. Find the measure of ∠𝑧
11. Find the measure of ∠𝑥
12. Find the sum of the interior angles ∠𝑥, ∠𝑦 and ∠𝑧 in the figure above.
x
z y
D
A B P
Q C R 81°
29°
Day 31 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 41
13. What do you discover about the sum in question 12 with respect to the triangle formed above?
Use the figure below to answer questions 14-20. FG ∥ HI and the two transversal lines intersect the pair
of parallel lines to form triangle XYZ.
14. Find the measure of ∠FXY
15. Find the measure of ∠FXZ
16. Find the measure of ∠𝑏
17. Find the measure of ∠𝑎
18. Find the measure of ∠𝑐
a
c b
X
H I
F G
Y Z
111°
28°
Day 31 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 42
19. Find the sum of these angles: ∠𝑎, ∠𝑏 and ∠𝑐
20. What does this tell you about the three angles in relation to triangle XYZ?
Day 31 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 43
Answer keys
Day 31:
1. ∠𝑦 = 44°
2. ∠𝑧 = 59°
3. ∠𝑥 = 77°
4. 180°
5. The sum of interior angles of the triangle add up to 180°
6.∠𝑦 = 81°
7. 99°
8. 99°
9. 29°
10. ∠𝑧 = 29°
11. ∠𝑥 = 70°
12.180°
13. The sum of interior angles of the triangle add up to 180°
14. 69°
15. 152°
16. ∠𝑏 = 69°
17. ∠𝑎 = 83°
18. ∠𝑐 = 28°
19. 180°
20. The sum of interior angles of the triangle add up to 180°
Day 31 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 44
In the figure below, AB ∥ CD and the two transversal lines intersect the pair of parallel lines to form
triangle JKL as shown below.
(a) Find the measure of ∠𝑎
(b) Find the measure of ∠𝑏
(c) Find the measure of ∠𝑐
(d) Find the sum of ∠𝑎, ∠𝑏 and ∠𝑐. What is your conclusion about that sum in relation to the triangle
formed above?
a
b c
J
C D
A B
K L
62°
47°
Day 31 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 45
Answer Keys
Day 31:
(a) ∠𝑎 = 62°
(b) ∠𝑏 = 47°
(c) ∠𝑐 = 71°
(d) ∠𝑎 + ∠𝑏 + ∠𝑐 = 62° + 47° + 71° = 180°.
The interior angles of the triangle add up 180°
Day 32 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 46
In the figure below, triangle PQR is formed between the pair of parallel lines AB and CD.
(a) Find the measure of ∠𝑦
(b) Find the measure of ∠BPR
(c) Find the measure of ∠𝑥
(d) Find the measure of ∠𝑧
(e) Compare the measure of ∠𝑥 to that of ∠𝑦, is there any relationship between the two angles?
x
z y
D
A B P
Q C R 79°
22°
Day 32 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 47
Answer Key Day 32:
(a) ∠𝑦 = 79°
(b) ∠𝐵𝑃𝑅 = 22°
(c) ∠𝑥 = 79°
(d) ∠𝑧 = 22°
(e)∠𝑥 = ∠𝑦 = 79° ; They are congruent.
Day 32 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 48
1. Label the plain paper provided as ABCD.
2. Fold the paper carefully at its center making sure the edge AB is aligned exactly on the edge CD as
shown below.
3. Using the pair of scissors provided, cut carefully the folded paper along the diagonal as shown below.
4. Remove the outer cut-out and open up the paper as shown below. What type of plane figure is
formed from the other cut-out?
A
B
C
D
A
B
C
D
D B
P
Day 32 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 49
5. Label the remaining vertex as P.
6. Using a ruler, measure 𝐵𝑃̅̅ ̅̅ and 𝐷𝑃̅̅ ̅̅ in inches on the cut out. What do you notice?
7. Using a protractor, measure angles ∠BDP and ∠DBP and compare their measures. What do you
notice?
Day 32 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 50
In this activity the students will work in groups of four to discover that an isosceles triangle has at least
two equal sides and consequently its base angles are congruent through simple paper folding and
cutting. The students in the respective groups will require an A5 size plain paper, a protractor, a pair of
scissors and a ruler. Emphasize that each procedure to be done carefully to guarantee accurate
observations.
Answer Keys Day 32:
1. No response
2. This is to ensure that the fold is straight and it connects the midpoint of edge AC to midpoint of edge
BD.
3. No response
4. Triangle
5. No response
6. 𝐵𝑃̅̅ ̅̅ = 𝐷𝑃̅̅ ̅̅
7. ∠BDP = ∠DBP
Day 32 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 51
Use the figure below to answer questions 1-5.
Isosceles triangle ABC is formed by the parallel lines XY and PQ. ∠CAY = ∠ABC = 𝜃.
1. Find the measure of ∠BAX in terms of 𝜃.
2. Find the measure of ∠ACB in terms of 𝜃.
3. Find the measure of ∠BAC in terms of 𝜃.
4. Express the sum of angles ∠ABC, ∠ACB and ∠BAC.
5. Compare the measures of ∠ABC to ∠ACB. What do you notice?
Day 32 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 52
Use the figure below to answer questions 6-11. The parallel lines JK and LM together with the two
transversal lines form triangle PQR as shown below. ∠JPQ = ∠KPR = 𝛼.
6. Find the measure of ∠QPR in terms of 𝛼.
7. Find the measure of ∠PQR in terms of 𝛼.
8. Find the measure of ∠PRQ in terms of 𝛼.
9. Identify two congruent interior angles in triangle PQR.
10. Hence, identify two equal edges on triangle PQR.
11. Using your responses from questions 9 and 10, give the type of triangle PQR.
Day 32 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 53
Use the figure below to answer questions 12-16. Triangle XYZ is formed between the parallel lines FG
and JK. ∠MXF = ∠GXN = β.
12. Find the measure of ∠MXN in terms of 𝛽.
13. Hence, find the measure of ∠YXZ in terms of 𝛽.
13. Find the measure of ∠FXY in terms of 𝛽.
14. Find the measure of ∠GXZ in terms of 𝛽.
15. Using the measure of ∠MXF, find the measure of ∠XZY.
16. Using the measure of ∠GXN, find the measure of ∠XYZ.
17. Compare ∠XZY to ∠XYZ. What is the relationship between the two angles?
18. Using the relationship between angles ∠XZY and ∠XYZ, identify two equal line segments from
triangle XYZ above.
19. Using information from questions 17 and 18 above, what type of triangle is triangle XYZ?
20. Give the major reason to support your response to question 19 above.
Day 32 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 54
Answer keys Day 32:
1. 𝜃
2. 𝜃
3. 180° − 2 𝜃
4. 180°
5. ∠ABC = ∠ACB = θ; The two angles are congruent.
6. 180° − 2𝛼
7. 𝛼
8. 𝛼
9. ∠PQR and ∠PRQ
10. PQ̅̅̅̅ and PR̅̅̅̅
11. Isosceles
12. 180° − 2𝛽
13. 180° − 2𝛽
14. 𝛽
15. 𝛽
16. 𝛽
17.∠XZY = ∠XYZ; The two angles are congruent
18. XY̅̅̅̅ and XZ̅̅̅̅
19. Isosceles
20 The base angles are equal; ∠XZY = ∠XYZ
Day 32 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 55
In the figure below isosceles triangle JKL is formed between the parallel lines AB and CD. ∠AJK =
∠AJM = β.
(a) Find the measure of ∠JKL in terms of 𝛽.
(b) Find the measure of ∠JLK in terms of 𝛽.
(c) Compare the measures of angles ∠JKL and ∠JLK. What do you discover?
J
C D
A B
K L
𝛽
𝛽
M
Day 32 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 56
Answer Keys
Day 32:
(a) ∠JKL = β
(b) ∠JLK = β
(c) ∠JKL = ∠JLK = β ; The two angles are congruent.
Day 33 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 57
1. ABC is an isosceles triangle. Line AB = 3 inches and line AC = 5 inches. Use the triangle to answer the
questions that follow.
a) Find the length of AD.
b) What is the length of BD?
c) Find the length of the side BC
d) If ∠𝐶𝐴𝐷 = 31°, What is the size of ∠𝐶𝐵𝐷
2. A line DF is 9 inches long. If G is its midpoint, find the size of line GF.
A D B
C
Day 33 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 58
Answer Key Day 4
1. a) 1 ∙ 5 𝑖𝑛𝑐ℎ𝑒𝑠
b) 1 ∙ 5 𝑖𝑛𝑐ℎ𝑒𝑠
c) 5 𝑖𝑛𝑐ℎ𝑒𝑠
d) 31°
2. 4 ∙ 5 𝑖𝑛𝑐ℎ𝑒𝑠
Day 33 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 59
1. Draw a line of length 4 inches and name it AB.
2. Place the protractor on line AB as shown the measure angle60°.
4. Remove the protractor and join point A and the mark with a straight line as shown below.
5. Measure a distance of 4 inches along the line you have drawn in 4 above, mark it and label it C as
shown.
6. Using a pencil and a ruler, join C and B with a straight line to get ∆𝐴𝐵𝐶 below
A B
A B
Day 33 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 60
7. Mark the midpoints of sides AB, AC and BC as D, E and F respectively.
8. Join the ∠𝐴 and F, ∠𝐶 and D then ∠𝐵 and E as shown below.
What do you notice about the intersection of the midpoints?
C
A B D
E F
C
A B D
E F
Day 33 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 61
In this activity, students are required to draw an equilateral triangle and its medians to study where and
how they meet. Students are required to work in groups of at least three. Each group is required to have
a plane paper, a pencil, a protractor and a ruler.
Answer Keys Day 33:
1-7. No response
8. They all meet at the same point
Day 33 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 62
Use the information below to answer questions 1 - 5.
In ∆𝑆𝑇𝑅, 𝑆𝑇 = 11 𝑖𝑛𝑐ℎ𝑒𝑠, 𝑇𝑅 = 8 𝑖𝑛𝑐ℎ𝑒𝑠 𝑎𝑛𝑑 𝑅𝑆 = 10 𝑖𝑛𝑐ℎ𝑒𝑠. The line segments AT, CR and BS are
the medians of ∆𝑆𝑇𝑅.
1. What is the length of BR?
2. Find the length of SC
3. What is the length of AR?
4. What is the length of AS?
5. Find the length of BT.
In questions 6 to 10. State whether the given statement is true or false.
6. A midpoint of a line divides it into two equal parts.
7. Medians of a triangle meet at two different points.
8. Medians of a triangle meet at one of its vertices.
9. Median of a triangle must run from one vertex and meet the opposite side at a right angle.
S
T
R
A
B
C
Day 33 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 63
10. Medians of a triangle meet at one point.
11. Draw the medians of the triangle given below.
Use the triangle below to answer questions 12 – 17
The Line segments AN, MB and CO are the medians of ∠𝑀𝑁𝑂.
12. Write an equation that relates AM and AF.
13. Write an equation that can relate AM and FM.
14. If FB is 3 ∙ 5 𝑖𝑛𝑐ℎ𝑒𝑠 long. What is the length of the side FN.
N M
F
A B
C
O
Day 33 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 64
15. Write an equation that relates MC and CN.
16.Write an equation that relates MC and MN.
17. Which name is given to the point marked F?
Use the triangle below to state whether the statements given questions 18 – 20 is true or false.
CF, BD and AE are the medians of the triangle.
18. AB =1
2𝐴𝐹
19. ∠𝐶𝐷𝑂 𝑚𝑢𝑠𝑡 𝑏𝑒 𝑒𝑞𝑢𝑎𝑙 𝑡𝑜 90°
20. CE ≠ EB
O
A B
C
D E
F
Day 33 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 65
Answer Key
Day 33
1. 4 inches
2. 5 ∙ 5 𝑖𝑛𝑐ℎ𝑒𝑠
3. 5 inches
4. 5 inches
5. 4 inches
6. True
7. False
8. False
9. False
10. True
11.
12. AM = AF
13. FM = 2AM
14. 7 Inches
15. MC = CN
16. MN = 2MN
17. Centroid
18. False
19. False
20. False
Day 33 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 66
1. Draw the medians of the following triangle identifying any resultant features created as a result of
drawing the medians.
S T
R
Day 33 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 67
Answer Keys
Day 33:
S T
R
Day 34 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 68
1. If a triangle is symmetrical about = 𝑥 , is their any rigit motion that can be realized in any form of
setup created by the triangle. Which one, explain.
2. One of the base angles of an Isosceles triangle is 40°, find the size of all other angles.
3. Can we have a base angle of an Isosceles triangle being 90°? Explain your answer.
4. Explain why one can view an equilateral triangle as an Isosceles triangle.
5. Two triangles with a common side have two corresponding vertices at equal distance from the
common side. What is the condition that such kind of set up will make a bigger triangle when the
common side is deleted?
Day 34 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 69
Answer Key
Day 34
1. Yes, reflection. One sid of the triangle below 𝑦 = 𝑥 is a reflection of the one above it or vise
versa.
2. 40° and 100°
3. No because the sum of the two base angles would be 180° before the third one is added. This
cannot be since the sum of all interior angles must be 180°.
4. An equilateral triangle has at least two equal angles and sides.
5. The two corresponding vertices must be on the same line as one of the ends of the common
side.
Day 34 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 70
1. On a plane paper, draw a straight line of length between 2 and 4 inches.
2. From one side of the drawn line, draw another line of the same length to meet at an acute angle
4. Connect the ends of the two lines to form a triangle.
5. Confirm that the triangle formed in an Isosceles triangle by measuring and writing their lengths.
6. Label the vertices.
7. Identify the base line and the base angles.
8. Measure the all interior angles.
9. Sum the angles and what do you get?
10. What is common about the measurements of the base angles?
11. Draw the medians of the lines, what do you notice?
Day 34 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 71
In this activity, students are required to draw an Isosceles triangle then prove that the base angles are
equal, the sum of interior angles is 180° and the medians intersect at a common point. Students will
work in groups of 5. Each group will be provided with a plane paper, a pencil, a ruler and a protractor.
Answer Keys Day 34:
1 – 4. No response
5. Answers will vary but two must sides must be approximately equal
6. No response
7 - 8. Answers may vary
9. 180°
10. They are equal
11. They intersect at the same point
Day 34 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 72
Use the information below to answer questions 1 - 7.
In the figure below, lines HE and AD are parallel. Angle 𝐹𝐺𝐸 = 61° and angle 𝐹𝐺𝐶 = 97°.
1. Find the size of angle EGC
2. Find the size of angle GCB
3. Find the size of angle HGB
4. Find the size of angle ABG
5. Find the size of angle GBC
6. Find the size of angle BGC
7. Find the sum of angles GBC, BCG and CGB.
A B C D
E
F
G H
Day 34 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 73
Use the information below to answer questions 8 - 12.
Consider the following triangle.
8. Identify the type of triangle.
9. Identify the points in each line that divides it into two equal parts.
10. Draw all the medians of the triangle.
11. Identify the number of points where they meet.
12.Identify if the point(s) above are inside or outside the triangle.
Day 34 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 74
Use the information below to answer questions 13 - 20.
In the figure below, line 𝑀𝐿 = 𝐾𝐿 and 𝑀𝑁 = 𝑁𝐾. KM = 24 in and ML = 20 in and angle 𝑀𝐿𝑁 = 37°.
13. Find the size of line NK.
14. Find the size of line KL.
15. Identify any two pairs of complementary angles.
16. Find the size of angle KLN.
17. Find the size of angle NKL
18. Find the size of angle NML
19. Compare the size of angles in 17 and 18 above.
20. Identify, if any, a rigid motion between triangles MNL and NKL.
K
L
M
N
Day 34 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 75
Answer Key
Day 34
1. 36°
2. 36°
3. 61°
4. 119°
5. 61°
6. 83°
7. 180°
8. Scalene Triangle
9. Answers may vary
10.
11. One
12. Inside
13. 12 in
14. 20 in
15. Angles NML and MLN
Angles NLK and LKN
16. 37°
17. 53°
18. 53°
19. The angles are equal to 53°
20. Reflection
Day 34 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 76
A triangle is symmetrical about 𝑥 −axis. Identify the 𝑦 −codinate of the point at which the medians
meet. Explain why.
Day 34 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 77
Answer Keys
Day 34:
The 𝑦 −coordinate is 0.
This is because one of the medians will lie of the 𝑥 −axis whose equation is 𝑦 = 0. Since the point of
intersection is shared among all the medians, it must satisfy the equation of each median including 𝑦 =
0, thus, the 𝑦 coordinate.
78
High School Math Teachers
Geometry
Weekly Assessment Package
Week 7
©2020HighSchoolMathTeachers
79
Week 7
Weekly Assessments
80
Week #7 1. Use the figure below to answer the questions that follow.
a) By supplementary angles property, find the size of ∠𝐵𝐶𝐸 . b) By alternate angles property, find the size of ∠𝐵𝐸𝐶. c) By alternate angles property, find the size of ∠𝐶𝐵𝐸. d) Find ∠𝐵𝐸𝐶 + ∠𝐵𝐶𝐸 + ∠𝐶𝐵𝐸
58°
A B
D
E
C F
G
55°
81
2. The triangle below is reflected through side
BC.
a) On the figure, draw the image.
b) What is the size of ∠𝐴𝐴′𝐶?
3. Use the triangle below to answer the
questions that follow.
a) Find the value of 𝑥.
b) Find the size of each base angle.
4. Line AB passes through points 𝐴(3, −2) and
𝐵(8,0). Line BC is perpendicular to AB.
a) Find the slope of BC.
b) Find the equation of BC.
5. Lines CD and EF are parallel. Line
CD passes through points 𝐶(4,6) and
𝐷(13,4). Line EF passes through
point 𝐹(5,1).
a) Find the slope of EF.
b) Find the equation of EF.
A B
C
56° (2𝑥 + 20)° ( 4𝑥 )°
82
6. Use the figure below to answer the questions
that follow.
a) Find the size of angle 𝑎.
b) Find the size of angle 𝑏.
158°
𝑎
𝑏
83
Week 7 - KEYS
Weekly Assessments
84
Week #7 KEY
1. Use the figure below to answer the questions that follow. a) By supplementary angles property, find the size of ∠𝐵𝐶𝐸 . 67° b) By alternate angles property, find the size of ∠𝐵𝐸𝐶. 58° c) By alternate angles property, find the size of ∠𝐶𝐵𝐸. 55° d) Find ∠𝐵𝐸𝐶 + ∠𝐵𝐶𝐸 + ∠𝐶𝐵𝐸
180°
58°
A B
D
E
C F
G
55°
85
2. The triangle below is reflected through side BC.
c) On the figure, draw the image.
d) What is the size of ∠𝐴𝐴′𝐶?
56°
3. Use the triangle below to answer the questions that follow.
c) Find the value of 𝑥.
10
d) Find the size of each base angle.
Each base is equal to 40°
4. Line AB passes through points 𝐴(3, −2) and 𝐵(8,0). Line BC is perpendicular to AB.
c) Find the slope of BC.
−5
2
d) Find the equation of BC.
2𝑦 = −5𝑥 + 15
5. Lines CD and EF are parallel. Line CD passes through points 𝐶(4,6) and 𝐷(13,4). Line EF passes through point 𝐹(5,1).
c) Find the slope of EF.
−2
9
d) Find the equation of EF.
𝑦 = −2
9𝑥 +
19
9
(2𝑥 + 20)° ( 4𝑥 )°
A B
C
56° 𝐴′
86
6. Use the figure below to answer the questions that follow.
c) Find the size of angle 𝑎.
158°
d) Find the size of angle 𝑏.
158°
158°
𝑎
𝑏
Day 36 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 87
1. Briefly describe the meaning of the following terms in your own words as used in geometry:
(a) Line segment
(b) Angle
(c) Ray
2. Sketch a diagram to show the following:
(a) End points of a line segment
(b) Perpendicular lines
Day 36 Bellringer Name ____________________________________
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Answer Keys
Day 36:
NB: Target the key words in the description of the terms
1. (a) A portion/part of a line between two endpoints
(b) The amount of turn/ space between two rays diverging from a common point or meeting
at a common point.
(c) A line having one endpoint and extending infinitely in the other direction.
2. (a)
(b)
The symbol for parallel lines must be shown.
Endpoint Endpoint
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HighSchoolMathTeachers.com©2020 Page 89
1. Draw a straight line segment of exactly three inches using the straightedge.
2. Label the line segment PQ as shown below.
3. Ensuring that the straightedge is aligned on segment PQ at the upper edge, draw another line
segment below PQ as shown below. It should be slightly longer than PQ.
4. Label point R on the new line segment as shown above.
5. Using the pair of compasses and taking point P as the center and radius PQ, carefully take the length
of PQ.
6. Using the same radius and now using R as the new center, make a mark on the new line segment.
Label the new point S as shown below.
7. What type of lines are PQ and RS?
8. Using a ruler measure the length of segment RS in inches.
9. Compare the lengths of RS to the length of PQ. What do you discover?
10. Is it correct to say that segment RS is a copy of segment PQ? Give a reason.
P Q
P Q
R
P Q
R S
Day 36 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 90
In this activity students will work in groups of four to copy a line segment using a straightedge, a ruler, a
pencil, a pair of compasses and an A4 size plain paper.
Answer Keys Day 36:
1. No response
2. No response
3. This is to ensure that PQ ∥ RS
4. No response
5. No response
6. No response
7. Parallel lines
8. RS = 3 in.
9. PQ̅̅̅̅ = RS̅̅̅̅
10. Yes, they two segments have the same length and they are parallel as well
Day 36 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 91
Bisect the line segments in questions 1-5. In each case use a straightedge and a pair of compasses only.
1.
2.
3.
A B
Q
P
K L
Day 36 Practice Name ____________________________________
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4.
5.
M N
R
S
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Bisect accurately the angles in questions 6-10 using a straightedge and a pair of compasses only. Label
the duplicate angles using suitable letters.
6.
7.
8.
A
B C
K
L M
P
Q
R
Day 36 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 94
9.
10.
Copy accurately the line segments in questions 11-15 to a different position using a straightedge and a
pair of compasses only. Label the duplicate segments using any appropriate letters.
11.
J
K L
X Y
Z
A B
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12.
13.
14.
Q
P
K L
M N
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15.
Copy accurately the angles in questions 16-20 to a different position using a straightedge and a pair of
compasses only.
16.
R
S
A
B C
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HighSchoolMathTeachers.com©2020 Page 97
17.
18.
19.
K
L M
J
K L
P
Q
R
Day 36 Practice Name ____________________________________
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20.
X Y
Z
Day 36 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 99
P
Q
M
Answer keys
Day 36:
1.
AM̅̅̅̅̅ = MB̅̅ ̅̅
2.
PM̅̅ ̅̅ = MQ̅̅̅̅̅
A B M
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HighSchoolMathTeachers.com©2020 Page 100
3.
KM̅̅̅̅̅ = ML̅̅ ̅̅
4.
MO̅̅̅̅̅ = ON̅̅ ̅̅
K L M
M N O
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HighSchoolMathTeachers.com©2020 Page 101
5.
RM̅̅̅̅̅ = MS̅̅ ̅̅
6.
R
S
M
A
B C
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7.
8.
K
L M
P
Q
R
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9.
10.
J
K L
X Y
Z
Day 36 Practice Name ____________________________________
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11.
12.
A B
C D
Q
P R
S
Day 36 Practice Name ____________________________________
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13.
14.
K L
M N
P
M N
Q
Day 36 Practice Name ____________________________________
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15.
16.
A
B C
R
S
P
Q
Day 36 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 107
17.
18.
K
L M
P
Q
R
Day 36 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 108
19.
20.
J
K L
X Y
Z
Day 36 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 109
Copy ∠KLM below using a straightedge and a compass only. Name the duplicate angle ∠PQR.
K
L M
Day 36 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 110
Answer Keys
Day 36:
The accuracy of the measure of ∠PQR should be ascertained; ∠KLM ≅ ∠PQR
P
Q R
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1. Given that C is the midpoint of line AB and that the length of AC is 3𝑥, what is the leghth of the line
AB?
2. Construct a perpendicular bisector to the line given below.
3. State whether the following statements are true or false.
a) A bisector of a line is also perpendicular to the line.
b) When constructing a line bisector, we should change the radius of the compass after drawing each
arc.
c) A bisector of a line passes through its midpoint.
A 3𝑥 C B
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Answer Key Day 37
1. 6𝑥
2.
3. a) True
b) False
c) True
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HighSchoolMathTeachers.com©2020 Page 113
1. Draw a 3 in straight line on a plain paper and label it AB.
2. Tie one end of the string to the pencil(make sure the string is tied close to the tip of the pencil)
3. Tie the other end of the string to a push pin and let the pushpin be held right at point A. Ensure the
length of the string between the push pin and the pensil is less than that of AB and more than half AB.
4. With the string fully stretched, draw a circle around point A as shown below.
5. Remove the string from point A and hold it on point B.
6. Draw another circle around point B as shown below.
A B
A B
Day 37 Activity Name ____________________________________
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7. Label the points of intersection of the two circles as C and D and join them with a straight line as
shown below.
8. Measure the angle of intersection of the lines AB and CD. What the value?
A B
C
D
Day 37 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 115
In this activity students are required to draw perpendicular lines using a string. Students will work in
groups of at least four and each group is required to have a string (which is more than 6 inches long ), a
pencil, a plain paper, a protractor, push pin and a straightedge.
Answer Keys
Day 37:
1-7. No response
8. 𝐴𝑏𝑜𝑢𝑡 90°
Day 37 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 116
Study the figure below and use it to answer questions 1 and 2.
1. Which construction tool might have been used to construct the line perpendicular to AB?
2. Is AB always perpendicular to ST.
3. When you are required to draw a line perpendicular to the given line at O, one is required ti draw an
arc or a circle as the first step. Therefore, draw a suitable circle as your first step in the process.
4. Construct a line perpendicular to the line MN using a compass and a straight edge
A B
S
T
O
Day 37 Practice Name ____________________________________
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5. State whether the following statement is true or false.
A perpendicular line always divides a line into two equal parts.
From question 6 to 12 construct a line which is perpendicular to the given line.(Leave all the marks)
6.
7.
8.
9.
Day 37 Practice Name ____________________________________
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10.
11.
12.
Day 37 Practice Name ____________________________________
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13. Use a straightedge and a compass to construct a line passing through point O and perpendicular to
line given below.
14. A student constructed two perpendicular lines below using a certain construction tool. Which
combination of construction tool was used if the student left all the marks.
15. The diagram below shows a construction of a line perpendicular to line KL. Complete the
construction.
. O
K L
Day 37 Practice Name ____________________________________
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16. Make the first two arcs you would make to construct a line perpendicular to line AB through point C.
17. Below is a diagram showing uncompleted construction of a line perpendicular to line MN through
point C. Using a compass and a straightedge, complete the construction.
18. The diagram below shows uncompleted construction of a line perpendicular to line AB through point
O. Use a compass and the straightedge to complete the construction.
A B C
M N C
O
Day 37 Practice Name ____________________________________
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In questions 19 and 20, use a string and a straightedge to construct a line perpendicular to the given line
segment.
19.
20.
Day 37 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 122
Answer Key Day 37
1. Compass and straightedge.
2. Yes
3.
4.
5. False
6.
7.
8.
O
Day 37 Practice Name ____________________________________
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9.
10.
11.
Day 37 Practice Name ____________________________________
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12.
13.
14. Reflective device and a straightedge
15.
16.
. O
K L
A B C
Day 37 Practice Name ____________________________________
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17.
18.
19.
M N C
O
Day 37 Practice Name ____________________________________
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20.
Day 37 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 127
1. Using a compass and a straightedge construct a line which is perpendicular to line AB.
A B
Day 37 Exit Slip Name ____________________________________
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Answer Keys
Day 37:
1.
A B
Day 38 Bellringer Name ____________________________________
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1. Transfer the following angles to the given points
(i).
(ii).
(iii).
2. Transfer the following points to the given locations
(i).
(ii).
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Answer Key Day 38
1. (i).
(ii).
(iii).
Day 38 Bellringer Name ____________________________________
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2. (i)
(ii).
Day 38 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 132
1. On the A4 plain paper, draw a horizontal line of between 4 to 6 inches.
2. Draw a line to intersect the horizontal one at acute angle at point A, about 1.5 in from the left hand
end of the horizontal line.
3. Label point B on the horizontal line about 2.5 to 3 inches from A. Label one side of the intersecting
line so that the acute angle in 2 above is angle DAB.
4. Place the fairly transparent paper to cover point A. Then trace lines AB and AD using a straight line.
5. Fold the paper along those lines drawn so that it forms an angle each to that of angle DAB with the
vertex A consciously visible.
6. Put the folded angle with the position of the vertex at B and one side of the folded angle lying along
the extension of the segment AB.
7. Draw a straight line of the other side of the folded angle. Label the side above BA as C
8. Measure angles DAB and CBA
9. Find the sum of the angles above. What do you deduce from the relation about line DA and BC
A B
D
Day 38 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 133
In this activity, we would like construct parallel lines using a paper folding technique. Students will work
in groups of 4. Each group will require a one A4 plain paper and another fairly transparent paper, a
pencil, protractor and a straight angle
Answer Keys
Day 38:
1 – 7.No response
8. Difference responses
9. They are parallel
Day 38 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 134
Use the following information to answer questions 1 - 3.
Transfer the angle at the given points.
1.
2.
3.
Day 38 Practice Name ____________________________________
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Use the following information to answer questions 4 - 9.
Draw lines parallel to the one given to pass through A using a set square.
4.
5.
6.
A
A
A
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7.
8.
9.
A
A
A
Day 38 Practice Name ____________________________________
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10.
11.
12.
A
A
A
Day 38 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 138
Use the following information to answer questions 13 – 18
Use angle transfer method to draw a parallel line to AC to pass through P.
13.
14.
15.
A
C
P
C
A P
C
A
P
Day 38 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 139
16.
17.
P
A
C
C
A P
Day 38 Practice Name ____________________________________
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18.
Use parallelogram method in question 19 and 20 to construct a line parallel to TS through point G.
19.
P
A
C
T
S
G
Day 38 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 141
20.
T
S
G
Day 38 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 142
Answer Keys
Day 38:
1.
2.
3.
Day 38 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 143
4.
5.
6.
A
A
A
Day 38 Practice Name ____________________________________
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7.
8.
9.
A
A
A
Day 38 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 145
10.
11.
12.
A
A
A
Day 38 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 146
13.
14.
15.
A
C
P
C
A P
C
A
P
Day 38 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 147
16.
17.
18.
P
A
C
P A
C
P
A
C
Day 38 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 148
19.
20.
T
S
G
T
S
G
Day 38 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 149
List at least three methods of drawing parallel lines
Day 38 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 150
Answer Keys
Day 38
Use of
(i). Reflecting devised
(ii). Strings and pins
(iii). Set squares
(iv). Angle transfer method (compass and a straightedge)
(v). Parallelogram method (compass and a straightedge)
Day 39 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 151
1. Copy line segment given below using a compass and a straightedge.
2. Use a compass and a straightedge to complete the construction of an angle bisector to ∠𝐴𝑂𝐶 below.
3. Construct a perpendicular bisector to the line segment given below.
A B
A B
O C
A
Day 39 Bellringer Name ____________________________________
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4. The diagram below shows partly completed construction of a line perpendicular to line AB through
point C. Complete the construction.
5. Draw a perpendicular line to AB through point O.
C
A B
A B O
Day 39 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 153
Answer Key
Day 39
1.
2.
3.
O C
A
A B
Day 39 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 154
4.
5.
C
A B
A B O
Day 39 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 155
1. Draw a straight line of length 3in at the center of semi-transparent plane paper.
2. Label the line as AB.
3. Fold the paper the paper across line AB so that the end A of the line overlaps with the end B.
4. Press the folded paper firmly to make a crease.
5. Unfold the paper and draw a line through the creases.
6. Measure the angle of intersection of the two lines. What do you get as the angle of intersection.
Day 39 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 156
In this activity students are required to construct a perpendicular lines through paper folding. Students
will work in groups of at least three. Each group is required to have a straightedge or a ruler, a pencil,
and a semi-transparent plane paper.
Answer Keys
Day 39:
1-5. No response
6. About 90°
Day 39 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 157
In questions 1 and 2, copy the given line segments.
1.
2.
3. Copy the angle given below.
4. Bisect the angle given below.
Day 39 Practice Name ____________________________________
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5. Bisect the angle given below.
In questions 6 to 9, construct a perpendicular bisector to the given line segment
6.
7.
8.
Day 39 Practice Name ____________________________________
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9.
In questions 10 to 13 construct a line perpendicular to the given line. (leave all the construction marks)
10.
11.
Day 39 Practice Name ____________________________________
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12.
13.
Day 39 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 161
14. Construct a perpendicular bisector to the line segment given below.
In questions 15 to 20, construct a line parallel to the given line that is passing through point marked P.
15.
16.
P
P
Day 39 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 162
17.
18.
19.
P
P
Day 39 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 163
20.
P
Day 39 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 164
Answer Key
Day 39
1.
2.
3.
4.
Day 39 Practice Name ____________________________________
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5.
6.
7.
Day 39 Practice Name ____________________________________
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8.
9.
10.
Day 39 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 167
11.
12.
13.
Day 39 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 168
14.
15.
16.
P
Day 39 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 169
17.
18.
19.
P
Day 39 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 170
20.
P
Day 39 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 171
1. Bisect ∠𝑀𝑂𝑁 below.
M
O N
Day 39 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 172
Answer Keys
Day 39:
M
O N
173
High School Math Teachers
Geometry
Weekly Assessment Package
Week 8
©2020HighSchoolMathTeachers
174
Week 8
Weekly Assessments
175
Week #8 1. Copy the line segment and the angle below.
Show all the marks
a)
b)
2. Construct a line bisector to the line segment and the
angle below. Show all the marks
a)
b)
A B
A B
176
3. Construct lines perpendicular the following lines. Show all the marks.
a)
b)
177
4. Use the figure below to answer the questions
that follow.
a) Use the property of supplementary angles to
find the size of ∠𝑋𝑇𝑌.
b) What is the size of ∠𝑌𝑋𝑇?
c) What is the size of ∠𝑋𝑌𝑇?
d) Solve ∠𝑋𝑇𝑌 + ∠𝑌𝑋𝑇 + ∠𝑋𝑌𝑇
5. The triangle below is reflected through side
MN.
a) Where will ∠𝑆 match?
b) Where will ∠𝑆𝑉𝑈 match?
c) Is ∠𝑆 = ∠𝑇?
6. Use the figure below to answer the questions that follow.
a) Find the value 𝑥.
b) Find the size of ∠𝐴.
S T
U
W X Y
z
71° 60°
V
U S T
(2𝑥)°
(𝑥 + 15)° (3𝑥 − 15)° A B
C
178
Week 8 - KEYS
Weekly Assessments
179
Week #8 KEY 1. Copy the line segment and the angle below. Show all the marks
c)
d)
2. 3Construct a line bisector to the line segment and the angle below. Show all the marks
c)
d)
A B
A B
A B
180
3. Construct lines perpendicular the following lines. Show all the marks.
a) b)
181
4. Use the figure below to answer the questions that follow.
e) Use the property of supplementary angles to
find the size of ∠𝑋𝑇𝑌.
49° f) What is the size of ∠𝑌𝑋𝑇?
71° g) What is the size of ∠𝑋𝑌𝑇?
60° h) Solve ∠𝑋𝑇𝑌 + ∠𝑌𝑋𝑇 + ∠𝑋𝑌𝑇
180°
5. The triangle below is reflected through side UV.
d) Where will ∠𝑆 match?
Onto ∠𝑇
e) Where will ∠𝑆𝑉𝑈 match?
Onto ∠𝑇𝑈𝑉
f) Is ∠𝑆 = ∠𝑇?
Yes 6. Use the figure below to answer the questions that follow.
c) Find the value 𝑥.
30
d) Find the size of ∠𝐴.
75°
S T
U
W X Y
z
71° 60°
V
U S T
(2𝑥)°
(𝑥 + 15)° (3𝑥 − 15)° A B
C
Day 41 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 182
1. Use a pair of compasses to draw circles with the following radii:
(a) 1.5 inches
(b) 2 inches
Day 41 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 183
(c) 2.2 inches
2. Study the diagram below and answer the following questions.
P
Q
R
Day 41 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 184
(a) Name the plane figures you see in the diagram.
(b) Which pane figure has its vertices touching the edge of the other figure?
(c) Which plane figure is inside the other?
(d) PQ̅̅̅̅ is one of the sides of the figure on the inside, what part of the figure on the outside does PQ̅̅̅̅
represent?
Day 41 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 185
Answer Keys Day 41:
1. (a)
(b)
Day 41 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 186
(c)
2. (a) A triangle and a circle
(b) The triangle
(c) The triangle
(d) Chord
Day 41 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 187
1. Using a pair of compasses, draw a circle of any convenient radius on the plain paper provided.
2. Label the center of the circle O.
3. Using a straightedge, draw a line segment to pass through the center O of the circle to construct the
diameter of the circle. Label it AB as shown below.
4. Using the compass, take the length of the radius; either OA̅̅ ̅̅ or OB̅̅ ̅̅ .
5. Without changing the width of the compass, endpoint B of the diameter AB as the center and make
two arcs that intersect the circle at two distinct points as shown below.
6. Label the points where the arcs intersect the circle as C and D as shown above.
B A O
C
B A O
D
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HighSchoolMathTeachers.com©2020 Page 188
7. Using a straightedge join point C to point D.
8. Similarly, join point A to point C and point A to point D respectively.
9. What is the name given to the plane figure formed inside the circle?
10. Using a protractor measure the size of ∠CAD, ∠ACD and ∠ADC. What do you notice about the
measures of these three angles?
11. Using a ruler, measure the lengths of AC̅̅̅̅ , AD̅̅ ̅̅ and CD̅̅̅̅ . What do you discover?
Day 41 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 189
In this activity students will work in groups of four. They will draw an equilateral triangle inscribed in a
circle using a straightedge and a pair of compasses. They will need a ruler calibrated in inches to
measure the lengths of the line segments, a protractor to measure the angles and an A4 plain paper.
Answer Keys Day 41:
1. The circle should be large enough but it should fit on the paper provided.
2. No response
3. No response
4. No response
5. No response
6. No response
7. No response
8. No response
9. A triangle
10. ∠CAD = ∠ACD = ∠ADC = 60°; The angles are congruent
11. AC̅̅̅̅ = AD̅̅ ̅̅ = CD̅̅̅̅ ; The line segments are equal
Day 41 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 190
Use a ruler and a compass to construct the largest possible equilateral triangles that can fit in each of
the given circles in questions 1-10. Use the radius indicated for your construction in each question.
1. Radius = 1 inch
2. Radius = 1.5 inches
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3. Radius = 1.3 inches
4. Radius = 0.8 inches
Day 41 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 192
5. Radius = 1.9 inches
6. Radius = 1.6 inches
Day 41 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 193
7. Radius = 1.4 inches
8. Radius = 1.7 inches
Day 41 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 194
9. Radius = 0.9 inches
10. Radius = 2.2 inches
Day 41 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 195
For questions 11-20, use a pair of compasses and a straightedge only to construct an inscribed triangle
in a circle of the indicated radius. Use a ruler to accurately take the radii with your compass.
11. Radius = 0.5 inches
12. Radius = 1.2 inches
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13. Radius = 1.8 inch
14. Radius = 0.7 inches
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15. Radius = 2.5 inches
16. Radius = 2.1 inches
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17. Radius = 0.6 inches
18. Radius = 2.4 inches
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19. Radius = 2 inches
20. Radius = 2.3 inches
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Answer keys
Day 41:
1.
2.
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3.
4.
5.
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6.
7.
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8.
9.
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10.
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11.
12.
13.
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14.
15.
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16.
17.
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18.
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19.
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20.
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Use a pair of compasses and a straightedge only to construct an inscribed triangle in a circle of radius 2
inches.
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Answer Keys Day 41:
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1. At what angle does the sides of the square meet?
2. What is a perpendicular bisector
3. A circle has a radius of 3.5in, what would be its diameter.
4. Draw a circle of radius 1.5 in.
5. Draw the perpendicular bisector of the following line
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Answer Key
Day 42
1. 90°
2. A line that divides another in to two equal parts and intersects it at a right angle
3. 7.0 𝑖𝑛
4.
5.
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1. On the A4 plain paper, draw a circle of radius 2.5 inches and mark the center O.
2. Draw diameter to the circle and label it AB where A and B are its endpoints.
3. Construct the perpendicular bisector of the line and let it meet at arcs of the circles at C and D
respectively.
4. Connect the points of the arcs where the perpendicular lines passes through to form a polygon.
5. Measure the sides of the polygon.
6. Which kind of polygon is the one in 4 above? State your reason.
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In this activity, we would construct a square inside a circle using a pairs of compass and a straightedge.
Students will work in groups of 3. Each group will require a plain paper, a pencil, a pair of compass and a
straight angle
Answer Keys
Day 42:
1 – 4.No response
5. Difference responses
6. Square. All sides are (approximately) equal
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Use the following information to answer questions 1 - 10.
Draw inscribed squares in the following given circles.
1.
2.
3.
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4.
5.
6.
7.
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8.
9.
10.
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Use the following statement to answer questions 11 – 18.
Consider a full diagram after inscribing a square in a circle
11. What is the name of the perpendicular bisector, of the diameter with respect to the square, that
spans between the vertices of the inscribed square drawn?
12. Explain your answer in 11 above.
13. What is the name of the perpendicular bisector of the diameter with respect to the circle that spans
between its vertices.
14. Explain your answer in 11 above.
15. Is the inscribed figure symmetrical?
16. Identify the lines along which it is symmetrical.
17. At what angle is the perpendicular bisector meeting the sides of the square?
18. The diameter and its perpendicular bisector divides the square into 4 equal parts, identify the name
of each part.
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Use the following information to answer questions 19 – 20.
Draw the inscribed square in the following in the circles whose diameter are given.
19. 2.8 in
20. 4.2 in
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Answer Keys Day 42:
1.
2.
3.
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4.
5.
6.
7.
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8.
9.
10.
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11. Diameter
12. It passes through the center of the diameter which is the center of the circle and spans between the
arcs of the circle
13. Diagonal of a square
14. It extends from one vertex of a square to the opposite one
15. Yes
16. Symmetrical about the diameter, its perpendicular bisector and along the perpendicular bisector of
opposite sides. Thus, 4 lines of symmetry
17. 45°
18. Right Isosceles triangle
19.
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20.
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Draw an inscribed square of radius 2 in.
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Answer Keys
Day 42
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1. Study the figure below and answer the questions that follow.
(a) Using a straightedge and a pencil join the points of intersection of the arcs and the circle in the order:
ABCDEFA.
(b) How many sides does the plane figure formed in (a) above have?
(c) How many angles does it have?
(d) What type of polygon is formed when the points are joined as in (a) above.
(e) Measure the following angles using a protractor and write down your conclusion.
∠A, ∠B, ∠C, ∠D, ∠E and ∠F
(f) Measure the lengths of the following line segments in inches using a using a ruler and write down
your conclusion.
𝐴𝐵̅̅ ̅̅ , 𝐵𝐶̅̅ ̅̅ , 𝐶𝐷̅̅ ̅̅ , 𝐷𝐸̅̅ ̅̅ , 𝐸𝐹̅̅ ̅̅ and 𝐹𝐴̅̅ ̅̅
(g) Basing on the conclusions in (e) and (f), is this a regular polygon or an irregular polygon?
A
B
C
D
E
F
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Answer Key Day 43:
(a)
(b) 6
(c) 6
(d) Hexagon
(e) All the angles are approximately congruent
(d) All the line segments have approximately equal lengths
(f) Regular polygon
A
B
C
D
E
F
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1. Draw a circle of any convenient radius on the tracing paper using a compass and label the center O.
2. Carefully fold the paper along the center O of the circle in such a way that the two semi-circles formed
coincide.
3. Label the line segment formed by the crease of the fold along the center of the circle AB, illustrated
above.
4. What is the name given to AB̅̅ ̅̅ with reference to the circle?
5. Firmly fold the paper in such a way that endpoint B coincides with the center O of the circle. This fold
forms two vertices of the polygon.
6. Label the two vertices C and D respectively as shown below.
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7. Similarly, firmly fold the paper in such a way that endpoint A coincides with the center O of the circle.
This fold forms two other vertices of the polygon.
8. Label the two vertices E and F respectively as shown above.
9. Using a straightedge and a pencil, join the points BCEAFDB in that order as shown below.
10. What is the name of the plane figure you have just constructed?
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In this activity students will work in groups of three to construct a regular polygon inscribed in a circle
using paper folding. Each group will require an A4 size tracing paper, a straightedge, a compass and a
pencil.
Answer Keys Day 43:
1. No response
2. No response
3. No response
4. Diameter
5. No response
6. No response
7. No response
8. No response
9. No response
10. Hexagon
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Use a ruler and a compass to construct the largest possible regular hexagon that can fit in each of the
given circles in questions 1-10. Use the radius indicated for your construction in each question.
1. Radius = 1 inch
2. Radius = 1.5 inches
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3. Radius = 1.3 inches
4. Radius = 0.8 inches
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5. Radius = 1.9 inches
6. Radius = 1.6 inches
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7. Radius = 1.4 inches
8. Radius = 1.7 inches
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9. Radius = 0.9 inches
10. Radius = 2.2 inches
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For questions 11-20, use a pair of compasses and a straightedge only to construct an inscribed regular
hexagon in a circle of the indicated radius. Use a ruler to accurately take the radii with your compass.
11. Radius = 0.5 inches
12. Radius = 1.2 inches
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13. Radius = 1.8 inch
14. Radius = 0.7 inches
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15. Radius = 2.5 inches
16. Radius = 2.1 inches
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17. Radius = 0.6 inches
18. Radius = 2.4 inches
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19. Radius = 2 inches
20. Radius = 2.3 inches
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Answer keys
Day 43:
1.
2.
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3.
4.
5.
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6.
7.
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8.
9.
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10.
11.
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12.
13.
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14.
15.
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16.
17.
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18.
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19.
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20.
Day 43 Exit Slip Name ____________________________________
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Use a compass and a straightedge only to construct a regular hexagon inscribed in a circle of convenient
radius.
Day 43 Exit Slip Name ____________________________________
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Answer Keys Day 43:
The circles will vary but the regular hexagon should be drawn accurately. All sides and angles of the
hexagon should be equal.
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1. The diagram below shows a partly completed construction of an inscribed equilateral triangle.
Complete the construction.
2. Below is a diagram of a square and its diagonals. What is the angle of intersection of the diagonals?
3. Construct the perpendicular bisector to the line segments given below.
a)
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b)
4. The diagram below shows a partly completed construction of a regular hexagon. Complete the
construction.
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Answer Key Day 4
1.
2. 90°
3. a)
b)
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4.
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1. Position the needle of the compass at 0 mark of the ruler and extend it up to an in mark.
2. Without changing the width of the compass in step 1, draw a circle in the middle of the plane paper.
3. Draw horizontal diameter to the circles.
4. Construct a perpendicular bisector of the diameter of the circle as shown.
5. Join the intersections of the diameter with the intersection of the perpendicular bisector.
6. Which shape is formed by the lines joining the diameter and the perpendicular bisector.
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In this activity, students will construct a square inscribed in a circle. Students are required to work in
groups at least three. Each group is required to have a pencil, a ruler, a plane paper and a compass.
Answer Keys
Day 44:
1-5. No response
6. Square.
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In questions 1 to 3, construct an inscribed square in the circle with the given radius.
1. Radius = 1.2in
2. Radius = 1.5 in
3. Radius = 0.75 in
In questions 4 to 7, you are given circles with their diameters, construct an inscribed square in each
circle.
4.
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5.
6.
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7.
In questions 8 to 13, construct an inscribed triangle in the circle with the given radius.
8. 0.75 in
9. 1 in
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10. 1.5 in
11. 2 in
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12. 1 ∙ 4𝑖𝑛
13. 1 ∙ 2𝑖𝑛
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From questions 14 to 19, you are given diameters of different circles. Draw the circle with the given
diameter and construct a regular hexagon inscribed in the circle.
14. 1.5 in
15. 2in
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16. 3in
17. 4in
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18. 2.8in
19. Construct a regular hexagon in the circle given below. O is the center of the circle.
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20. A pesticide manufacturing company designed a cylindrical can for storing a pesticide. They decided
to make a regular hexagonal hole at its circular top such that the vertices of the hole are on the
circumference of the circular top. If the can had a radius of one inch, draw the top part alone and
construct the hexagonal hole.
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Answer Key Day 44
1.
2.
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3.
4.
5.
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6.
7.
8.
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9.
10.
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11.
12.
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13.
14.
15.
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16.
17.
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18.
19.
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20.
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1. The circle below has a radius of 1inch. Construct an inscribed hexagon in the circle.
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Answer Keys
1.
283
High School Math Teachers
Geometry
Weekly Assessment Package
Week 9
©2020HighSchoolMathTeachers
284
Week 9
Weekly Assessments
285
Week #9 1. Construct an equilateral triangle inscribed in the
circle below.
2. Construct regular hexagon inscribed in the circle
below.
3. Construct squares inscribed in the circles below.
a)
b)
4. Construct perpendicular bisectors to the
following lines.
a)
b)
286
5. Line 𝐿1 passes through points 𝑋(−2, −6)
and 𝑌(−1,3). At point y, 𝐿2 intersects 𝐿1 at a
right angle.
a) Find the slope of 𝐿2.
b) Find the equation of 𝐿2.
6. Lines AB and CD are parallel. The equation of
AB is 5𝑦 = 7𝑥 − 36. Line CD passes through
point 𝐶(4,6).
a) Find the slope of CD.
b) Find the equation of CB.
287
Week 9 - KEYS
Weekly Assessments
288
Week #9 KEY 1. Construct an equilateral triangle inscribed in the circle below.
2. Construct regular hexagon inscribed in the circle below.
3. Construct squares inscribed in the circles below.
c)
d)
4. Construct perpendicular bisectors to the following lines. a)
b)
289
5. Line 𝐿1 passes through points 𝑋(−2, −6) and 𝑌(−1,3). At point Y, 𝐿2 intersects 𝐿1 at a right angle.
c) Find the slope of 𝐿2.
−1
9
d) Find the equation of 𝐿2.
9𝑦 = −𝑥 + 26
6. Lines AB and CD are parallel. The equation of AB is 5𝑦 = 7𝑥 − 36. Line CD passes through point 𝐶(4,6).
c) Find the slope of CD.
7
5
d) Find the equation of CB.
5𝑦 = 7𝑥 + 2
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Questions:
1. In the figure below lines PQ and RS are parallel. State whether the following angles are
corresponding, alternate interior or alternate exterior angles.
a) ∠4 and ∠5
b) ∠1and ∠5
2. What is the value of z?
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3. What is the sum of angles x, y and z?
4. Define triangle!
5. Find the measure of angle y.
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6. In the figure below isosceles triangle JKL is formed between the parallel lines AB and CD. Find the
value of angle ∠𝐽𝐿𝐾in terms of 𝛽.
7. ABC is an isosceles triangle. Line AB = 12 cm and line AC = 16 cm. Find the length of BD.
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8. In ∆𝑆𝑇𝑅, 𝑆𝑇 = 20 cm, 𝑇𝑅 = 16 cm 𝑎𝑛𝑑 𝑅𝑆 = 18 cm. The line segments AT, CR and BS are the
medians of ∆𝑆𝑇𝑅. What is the length of SC?
9. Draw the medians of the following triangle identifying any resultant features created as a result
of drawing the medians.
10. One of the base angles of an Isosceles triangle is 50°, find the size of all other angles.
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11. Bisect the line segment. Use a straightedge and a pair of compasses only.
12. Define line segment!
13. State whether the following statements are true or false.
a) A bisector of a line is also perpendicular to the line.
b) A bisector of a line passes through its midpoint.
14. List 3 main methods that are used to construct parallel lines.
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15. Use a compass and a straightedge to complete the construction of an angle bisector to ∠𝐴𝑂𝐶
below.
16. What is the name given to the plane figure formed inside the circle?
17. Define an inscribed triangle.
18. A circle has a radius of 4 cm, what would be its diameter?
19. Draw inscribed square in the circle.
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20. Here we have a square and its diagonals. What is the angle of intersection of the following
diagonals?
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Answers:
1.
a) Alternate interior angles
b) Corresponding angles
2. 𝑧 = 59°
3. 180°
4. Triangle is a plane figure bounded by three line segments to form its edges and three vertices
formed between two adjacent edges.
5. 𝑦 = 79°
6. ∠𝐽𝐿𝐾 = 𝛽
7. 𝐵𝐷 = 6𝑐𝑚
8. 𝑆𝐶 = 10𝑐𝑚
9.
10. 50° and 80°
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11.
12. Line segment is a portion of a line between two endpoints.
13.
a) True
b) True
14.
1) The use of a set square
2) The use of angle transfer method
3) The use of parallelogram method
15.
16. A triangle.
17. Inscribed triangle is a triangle drawn inside another plane figure such that the vertices of the
triangle touch the edge of the plane figure.
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18. 8cm
19.
20. 90°