Geometry Unit 4 Note Sheets Date Name of Lesson...
Transcript of Geometry Unit 4 Note Sheets Date Name of Lesson...
Geometry Unit 4 Note Sheets
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Date Name of Lesson
Classifying Triangles 4.1
Angles of Triangles 4.2
Inequalities in One Triangle 5.3
Constructing Incenter (Angle Bisectors)
Constructing Circumcenter (Perpendicular Bisectors)
5.1, 5.2
Congruent Triangles 4.3
Quiz
Proving Triangles Congruent – SSS, SAS, ASA, AAS, HL 4.4, 4.5
Use http://www.mathopenref.com/congruentaaa.html to show why AAA doesn’t work
Use http://www.mathopenref.com/congruentssa.html to show why ASS doesn’t work
Quiz
Isosceles and Equilateral Triangles 4.6
Congruence Transformations 4.7
Practice Test
Unit Test
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4.1 Classifying Triangles Notes
Guided Practice
1. Classify each triangle by their angles.
Your Turn
2.
Guided Practice
Classify each triangle by their sides.
3. 4.
Your Turn
Classify each triangle by their sides.
5. ∆𝐴𝐵𝐶
6. ∆𝐵𝐷𝐶
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Guided Practice
7. If point 𝑀 is the midpoint of 𝐽�̅�, classify ∆𝐽𝐾𝑀 as equilateral, isosceles, or scalene. Explain your reasoning.
Your Turn
8. If 𝑌 is the midpoint of 𝑉𝑋̅̅ ̅̅ , and 𝑊𝑌 = 3.0 𝑢𝑛𝑖𝑡𝑠, classify ∆𝑉𝑊𝑌 as equilateral, isosceles, or scalene.
Explain your reasoning.
Guided Practice
9. Find the measures of the sides of isosceles triangle 𝐴𝐵𝐶.
Your Turn
10. Find the measures of the sides of the isosceles triangle 𝐾𝐿𝑀 with base 𝐾𝐿̅̅ ̅̅ .
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4.2 Angles of Triangles Notes
Guided Practice
Find the measure of the numbered angles.
1. 2.
Your Turn
3. 4.
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Guided Practice
5. Find the measure of ∠𝐹𝐿𝑊. 6. Find the measures of the numbered angles.
Your Turn
7. Find the measure of the exterior angle shown. 8. Find the measures of the numbered angles.
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Guided Practice
Is it possible to form a triangle with the given side lengths? If not, explain why not.
1. 5 cm, 7 cm, 10 cm 2. 3 in, 4 in, 8 in
Your Turn
3. 6 m, 14 m, 10 m
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5.3 Inequalities in One Triangle
Guided Practice
1. Use the exterior angle theorem to name angles that have measures less than 𝑚∠4.
2. Use the exterior angle theorem to name angles that have measures less than 𝑚∠7.
Your Turn
3. Use the exterior angle theorem to name angles that have measures less than 𝑚∠2.
4. Use the exterior angle theorem to name angles that have measures less than 𝑚∠9.
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Guided Practice
List the angles and sides of each triangle in order from smallest to largest.
1. 2.
Your Turn
3. 4.
Guided Practice
List the angles and sides of each triangle in order from smallest to largest.
5. 6.
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5.1, 5.2 Constructing Incenter (Angle Bisectors)
Guided Practice
1. Construct the angle bisector of each angle to find the Incenter. (Draw circle inside with the center at the
incenter.)
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5.1, 5.2 Constructing Incenter (Angle Bisectors)
Guided Practice
1. Construct the perpendicular bisector of each angle to find the Circumcenter. (Draw circle around the outside
with the center at the circumcenter.)
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4.3 Congruent Triangles Notes
Guided Practice
1. Show that the polygons are congruent by identifying all the congruent corresponding parts. Then write a
congruence statement.
2.
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Corresponding Parts of Congruent Triangles are Congruent (CPCTC)
Guided Practice
3. In the diagram ∆𝐴𝐵𝐶 ≅ ∆𝐷𝐹𝐸. 4. In the figure, ∆𝐿𝑀𝑁 ≅ ∆𝑄𝑅𝑆.
Find the values of 𝑥 and 𝑦. Find the values of 𝑥 and 𝑦.
Your Turn
5. In the diagram ∆𝐼𝑇𝑃 ≅ ∆𝑁𝐺𝑂. Find the values of 𝑥 and 𝑦.
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4.4, 4.5 Proving Triangles Congruent – SSS, SAS, ASA, AAS, HL Notes
Side-Side-Side (SSS) Congruence
Side-Angle-Side (SAS) Congruence
Angle-Side-Angle (ASA) Congruence
Angle-Angle -Side (AAS) Congruence
Hypotenuse-Leg (HL) Congruence
Guided Practice
Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove
congruence, write not possible.
1. 2. 3.
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Your Turn
4. 5. 6.
7. 8. 9.
Guided Practice
Use the Distance Formula and SSS Congruence Postulate to show that ∆𝐴𝐵𝐶 ≅ ∆𝐷𝐸𝐹.
10.
Your Turn
11.
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4.6 Isosceles and Equilateral Triangles Notes
Guided Practice
1. Name two unmarked congruent angles.
2. Name two unmarked congruent segments.
Your Turn
3. Name two unmarked congruent angles.
4. Name two unmarked congruent segments.
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Guided Practice
5. Find each measure.
𝑚∠𝑌
𝑌𝑍
Your Turn
6. Find each measure.
𝑚∠𝑀
𝑃𝑁
Guided Practice
7. Find the value of x.
8. Find the value of y.
Your Turn
9. Find the value of x.
10. Find the value of y.
Guided Practice
Find the value of each variable.
11. 12.
Your Turn
13. 14.
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Use SAS to prove triangles
congruent.
4.7 Congruence transformations
Use SSS to prove triangles
congruent.
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5. Graph A(2,2), B(4, 7), C(6,2) and D(2,-2), F(4, -7), G(6, -2) on the same axis. Identify transformation
and prove triangles are congruent.
6. Determine whether ∆𝑻𝑱𝑫 ≅ ∆𝑺𝑬𝑲 given T(-4, -2), J(0, 5), D(1, -1), S(-1, 3), E(3, 10),
and K(4, 4). Explain and identify transformation. (Verify by using SSS,SAS,ASA, HL or AAS)