4-5 Isosceles and

Equilateral Triangles

• The congruent sides of an isosceles triangle are its legs• The third side is the base• The two congruent legs form the vertex

angle• The other two angles are the base

angles

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

If two angles of a triangle are congruent , then the sides opposite those angles are congruent

Problem 1: Using the Isosceles Triangle Theorems

Theorem 4-5If a line bisects the vertex angle of an isosceles triangle, then the line is also the perpendicular bisector of the base

Problem 2: Using Algebra

What is the value of x?

Corollary: is a theorem that can be proved easily using another theorem.

A corollary is a theorem, so you can use it as a reason in a proof.

Corollary to Theorem 4-3

If a triangle is equilateral, then the triangle is equiangular.

Corollary to Theorem 4-4

If a triangle is equiangular, then the triangle is equilateral.

Problem 3: Finding Angle MeasuresWhat are the measures of <A, <B, and <ADC in the photo?