4.7 Use Isosceles and Equilateral Triangles

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# 4.7 Use Isosceles and Equilateral Triangles - PowerPoint PPT Presentation

4.7 Use Isosceles and Equilateral Triangles. Define Isosceles . A triangle is isosceles iff it has two or more congruent sides (yes an equilateral triangle is also isosceles). Isosceles Triangle. vertex. Leg. Leg. base angle. base angle. Base. A. C. B.

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## 4.7 Use Isosceles and Equilateral Triangles

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### 4.7 Use Isosceles and Equilateral Triangles

Define Isosceles
• A triangle is isosceles iff it has two or more congruent sides (yes an equilateral triangle is also isosceles)
Isosceles Triangle

vertex

Leg

Leg

base angle

base angle

Base

A

C

B

Isosceles Triangle Theorem (Base Angles Theorem)
• If two sides of a triangle are congruent (isosceles triangle), then the angles opposite them are congruent

K

J

M

L

2. Draw JM

3. MK = ML

~

4. JK = JL

~

5. JM = JM

~

6. JMK = JML

~

7. < K = <L

~

Given: JK = JL

Prove <K = <L

~

R

S

1. Definition of a midpoint

1. Define M as the midpoint of the base

2. Two points determines a line

~

3. Definition of a midpoint

4. Given

5. Reflexive Property

6. SSS

7. CPCTC

A

C

B

Converse of the Isosceles Triangle Theorem (Converse of the Base Angles Theorem)
• If two angles of a triangle are congruent, then the sides opposite them are congruent
Corollaries
• If a triangle is equilateral, then it is equiangular
• If a triangle is equiangular, then it is equilateral
• If a triangle is equilateral (and equiangular) then it is a regular triangle
• If a triangle is equilateral (and equiangular) then the angles are 60°
Homework
• Page 267/1, 2, 4-6, 8-10, 12-14, 19, 26-29, 35, 36, 52, 54, 56