1. 4.4 The Isosceles Triangle Theorems
Geometry
4.4 The Isosceles Triangle Theorems

2. Isosceles Triangle
Vertex Angle
Leg
Leg
Base Angle
Base
Base Angle

3. The Isosceles Triangle Theorem
If two sides of a triangle are congruent, then the angles opposite those sides are congruent.
Iso Thm.

4. Corollary 1 An equilateral triangle is also equiangular.
Why does this come from the Isosceles Triangle Theorem?

5. Corollary 2
An equilateral triangle has three 60o angles.

6. Converse to Isosceles Triangle Theorem
If two angles of a triangle are congruent, then the sides opposite those angles are congruent.
Converse to Iso Thm.
2 ways to remember which is which…

7. Corollary
An equiangular triangle is also equilateral.

8. 5. 6.
100 x x 3x x 3x x x
100 7. 8. 9. x 50 70 x 70 50 x 62 62 x x x

9. 3. Given: Prove: Given Vert. angles congruent Transitive 1. 2. 4. 4.F E D 4 3 2 1
Given:
Prove: 1.
Statements
Reasons
Given 2.
Vert. angles congruent 3.
Transitive 4. 4.
2. vert 3.
Given:
Prove:

10. Example 1: a) If m<1 = 20, then m<3 = ____.
m<4 = ____ and m<5 = ____.
b) If m<1 = x, then m<3 = ____. 4 3 5 2 1

11. Example 2
Find x.
74o 10 10 x 12

12. Example 3
Solve for x.
40o
40o
5x - 8
2x + 7

13. ~ ~ 4) Given: M is the midpoint of JK 1 = 2 Prove: JG = MK 7 7 J M 1 2
1 = 2
Prove: JG = MK ~ 7 7 ~ J M 1 2 G K