Isosceles, Equilateral, and Right Triangles

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Isosceles, Equilateral, and Right Triangles

• Chapter 4.6

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Isosceles Triangle Theorem

• Isosceles ? ? The 2 Base ?s are ?
• Base angles are the angles opposite the equal
  sides.

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Isosceles Triangle Theorem
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Isosceles Triangle Theorem
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Sample Problem

• Solve for the variables
• m?A 32
• m?B (4y)
• m?C (6x 2)

32 32 4y 180 4y 64 180 4y
116 y 29
6x 2 32 6x 30 x 5
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Lesson 6 Ex2
Find the Measure of a Missing Angle
120o
30o
30o
30o
75o
75o
180o 120o 60o
180o 30o 150o
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Lesson 6 CYP2
A. 25 B. 35 C. 50 D. 130

1. A
2. B
3. C
4. D

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Lesson 6 CYP3
A. Which statement correctly names two congruent
angles?

1. A
2. B
3. C
4. D

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Lesson 6 CYP3
B. Which statement correctly names two congruent
segments?

1. A
2. B
3. C
4. D

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Equilateral Triangle Theorem

• Equilateral ? ? Equiangular

Each angle 60o !!!
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Lesson 6 Ex4
Use Properties of Equilateral Triangles
Linear pair Thm.
Substitution
Subtraction
Answer 105
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Lesson 6 CYP4
A. x 15 B. x 30 C. x 60 D. x 90

1. A
2. B
3. C
4. D

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Lesson 6 CYP4
A. 30 B. 60 C. 90 D. 120

1. A
2. B
3. C
4. D

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Dont be an ASS!!!

• Angle Side Side does not work!!!
• (Neither does ASS backward!)
• It can not distinguish between the two different
  triangles shown below.

However, if the angle is a right angle, then they
are no longer called sides. They are called
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Hypotenuse-Leg ? ? Theorem

• If the hypotenuse and one leg of a right triangle
  are congruent to the corresponding parts in
  another right triangle, then the triangles are
  congruent.

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?ABC ? ?XYZ Why?HL ? ? Theorem
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Prove ?XMZ ? ?YMZ
Step
Reason
Given
Given
m?ZMX m?ZMY 90o
Def of ? lines
Reflexive
HL ? ? Thm
?ZMX ? ?ZMY
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Corresponding Parts of Congruent Triangles are
Congruent

• Given ?ABC ? ?XYZ
• You can state that
• ?A ? ?X
• ?B ? ?Y
• ?C ? ?Z

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Suppose you know that ?ABD ? ?CDB by SAS ? ? Thm.
Which additional pairs of sides and angles can
be found congruent using Corr. Parts of ? ?s are
??
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Lesson 6 CYP1
Complete the following two-column proof.
Proof
Reasons
Statements
1. Given
1.
2. Isosceles ? Theorem
2.
3.
3. Given
4.
4. Def. of midpoint
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Lesson 6 CYP1
Complete the following two-column proof.
Proof

1. A
2. B
3. C
4. D

SAS ? ? Thm.
Corr. Parts of ? ?s are ?
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Homework
Video C

• Ch 4-6
• pg 248
• 1 10, 14 27, 32, 33, 37 39, 48

Reminder! Midpoint Formula