1. The Isosceles Triangle Theorems
Section 4-4
The
Isosceles Triangle
Theorems

2. Isosceles Diagram:
Vertex Angle
Base

3. Description of Parts:
Legs: the congruent sides
Base: non-congruent side; opposite the vertex angle
Base Angles: the two ’s formed by the base and one of the congruent sides
Vertex Angle:  formed by the  sides

4. The Isosceles Triangle Theorem
If two sides of a triangle are congruent, then the angles opposite those sides are congruent. A B C
So…

5. In other words, Base angles of an isosceles triangle are congruent!

6. An equilateral triangle is also equiangular.
Corollaries:
An equilateral triangle is also equiangular.
An equiangular triangle is also equilateral.
An equilateral triangle has three 60 degree angles.

8. Corollary:
The bisector of the vertex angle of an isosceles triangle is perpendicular to the base at its midpoint. A B C M

9. cONVERSE Isosceles Triangle Theorem
If two angles of a triangle are congruent, then the sides opposite those angles are congruent. A B C
So…