1. 4.7 Use Isosceles and Equilateral Triangles

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

3. Isosceles Triangle
vertex
Leg
Leg
base angle
base angle
Base

4. Isosceles Triangle Theorem (Base Angles Theorem)
If two sides of a triangle are congruent (isosceles triangle), then the angles opposite them are congruent A B C

5. ~ J K L
Given: JK = JL
Prove <K = <L ~ M S R
1. Define M as the midpoint of the base
1. Definition of a midpoint
2. Draw JM
2. Two points determines a line ~
3. MK = ML
3. Definition of a midpoint
4. JK = JL ~
4. Given
5. JM = JM ~
5. Reflexive Property
6. JMK = JML ~
6. SSS
7. < K = <L ~
7. CPCTC

6. Use the Isosceles Triangle Theorem

7. 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 B C A

8. 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°

9. Homework
Page 267/1, 2, 4-6, 8-10, 12-14, 19, 26-29, 35, 36, 52, 54, 56