4.1 Warm up 1. Using deductive reasoning prove the following: 4x -6 = 2(x + 9) 2) 6, 17, 28, 39….....
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Transcript of 4.1 Warm up 1. Using deductive reasoning prove the following: 4x -6 = 2(x + 9) 2) 6, 17, 28, 39….....
![Page 1: 4.1 Warm up 1. Using deductive reasoning prove the following: 4x -6 = 2(x + 9) 2) 6, 17, 28, 39….. Find the function rule and the 50th term 3) With parallel.](https://reader035.fdocuments.net/reader035/viewer/2022072006/56649f575503460f94c7b421/html5/thumbnails/1.jpg)
4.1 Warm up
1. Using deductive reasoning prove the following:
4x -6 = 2(x + 9)
2) 6, 17, 28, 39….. Find the function rule and the 50th term
3) With parallel lines, certain relationship exist for the type of angles formed. List the type of angles that are created and their relationship.
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Answers
1) 4x-6 = 2(x+9) Given
4x-6 = 2x + 18 Distributive Prop
2x – 6 = 18 Subtraction prop. of equality
2x = 24 Addition prop. of equality
x = 12 Division prop. of equality
2) 6, 17, 28, 39…… nth term = f(n) = 11n – 5 50th term = 545
3) Vertical angles, corresponding angles, alt. exterior, alt interior are congruent
Same side interior, same side exterior, linear pairs add to 180
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Sub groups -Scalene Triangle no congruent sides.
Equilateral Triangle all sides are congruent.
Isosceles Triangle at least 2 congruent sides.
Triangles- Come in 3 types: Acute: Obtuse: Right:
An acute triangle has 3 acute angles
An obtuse triangle has 1 obtuse angle
A right triangle has 1 right angle.
You can have Scalene and Isosceles of each type of triangle!
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Triangles
Acute Obtuse Right
Scalene Isosceles
Equilateral
Scalene Isosceles Scalene Isosceles
List each type of triangle
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TrianglesSketch each type of triangle in the box
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Ex. 1 - Triangles
How do I sketch, label, and mark each figure?A) Right Isosceles triangle SUN
with SU = UN.
B) Obtuse Isosceles triangle SEA
with SE = EA.
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Triangles class work!
Page 64-65 Questions #2-20
More to come……stay tuned!
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4.1 Triangle Congruence
Year 2 Geometry
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Materials
You will need: Protractor Scissors
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Investigation #1
Draw a triangle using your straight edge of the protractor. Make a variety of sizes!
Measure each angle of the triangle to the nearest 10°. The sum of the interior angles equals to ?
Cut out the triangle (around the perimeter). Cut 2 of the vertices (angles) from the triangle. Line up all three vertices. What do you notice?
180°
They form a line. (180°)
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Investigation #1 – continued
Paste the three vertices lined up in your notes and complete the following conjecture.
Triangle Sum Conjecture
The sum of the measures of the interior angles in every triangle is _______.180°
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Third Angle Conjecture
If two angles of one triangle are equal in measure to two angles in another triangle, then the third angle in each triangle is ___________________________?equal in measure
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Example #1
52°55°
x
73
180107
1805552
x
x
x
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Example #2
120°
130°
100°
z
60°
50°
x
110
18070
70
180110
1805060
z
z
x
x
x
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Example #3
5.45
1824
18024
180927
x
x
x
xxx
C.B, mA, mm Find
x 2x-9
x+7
A
B
C
82
5.52
5.45
Cm
Bm
Am
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Example #4
w. Find
66
1322
180248
18048
x
x
x
xx
48°
w
xx
24
9066
w
w
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Example #5
C.B, mA, mm Find
15
1359
180459
18072254133
x
x
x
xxx
3x+13 2x+7
4x+25
A C
B
37
85
58
Cm
Bm
Am
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Example 6
With a partner create your own problem with triangles similar to the previous examples to share with your group.
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Summary
Write the Triangle Sum Conjecture in your own words.
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In – Class Work
Lesson 4.1 – workbook Homework: Triangle Sum HW pg 201-202
2-5,8,9, 14-16