1. Theorems: Isosceles Triangles
Isosceles Triangles have two congruent sides (legs) and a third side (base)
leg
leg
base

2. Isosceles Triangle
Vertex angle
The angles at the base are called base angles and the angle opposite the base is the vertex angle
Base angles

3. What we know about them:P
<PRS cong. <PSR
Seg.PQ bisects <RPS
Seg.PQ bisects Seg.RS
Seg.PQ is perp. to Seg.RS at Q
Triangle PQR is congruent to Triangle PQS R Q S

4. Isosceles Triangle TheoremP
If two sides of a triangle are congruent, then the angles opposite those sides are congruent.
In other words, if PR is congruent to PS, then <R is congruent to <S R Q S

5. Isosceles Triangle CorollariesP
An equilateral triangle is also equiangular
An equilateral triangle has three 60 degree angles.
The bisector of the vertex angle of an isosceles triangle is perpendicular to the base at its midpoint. R S Q

6. Theorem 4-2 P
If two angles of a triangle are congruent, then the sides opposite those angles are congruent. R S Q

7. Corollary
An equiangular triangle is also equilateral.