1. Isosceles Triangles A B C
1. What does this example show about the base of an Isos. Triangle?
Legs: the congruent sides
Vertex Angle
Base: third side
Base Angles
Theorem: The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base. F E D G
We will prove this theorem later.

2. A C B
Isosceles Triangle Theorem:
If two sides of a triangle are congruent, then the angles opposite those sides are congruent.
Converse of the Isosceles Triangle Theorem: D E F
If two angles of a triangle are congruent, then the sides opposite the angles are congruent.
Two sides of a triangle are congruent if and only if the angles opposite those sides are congruent.

3. If a triangle is equilateral, then it is equiangular.
If a triangle is equiangular, then it is equilateral. A B C
Examples: Solve for x, y and z. x y 63 o z c v
116 o
Solve for b, c, w, v. b w

4. 1. The base of an Isosceles Triangle does not mean it is the bottom
1. The base of an Isosceles Triangle does not mean it is the bottom. The Base is not controlled by gravity on geometric figures, contrary to most student’s beliefs.
Answer to Examples
X = 27° y = 90° z = 63°
V = 32° w = 32° b = 64° c = 26°