Objective: To use and apply properties of isosceles triangles. Chapter 4 Lesson 5 Objective: To use and apply properties of isosceles triangles.

The congruent sides of an isosceles triangle are its legs The congruent sides of an isosceles triangle are its legs. The third side is the base. The two congruent sides 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 Isosceles Triangle Theorem If two angles of a triangle are congruent, then the sides opposite the angles are congruent.                            

Theorem 4-5   The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base.              and     bisects .

Example 1: Proofs D AAS CPCTC Given: bisects Prove: Given A A S Def. of bisector S Reflex. Prop. AAS CPCTC

Example 2: Proofs D SSS CPCTC Given: bisects Prove: Given S S S Def. of segment bisector S S Reflex. Prop. SSS CPCTC

Example 3: Using Algebra Find the values of x and y. By Theorem 4-5, you know that           , so x = 90. ∆M L N is isosceles, so    and

If a triangle is equilateral, then the triangle is equiangular. Corollary to Theorem 4-3 If a triangle is equilateral, then the triangle is equiangular.

If a triangle is equiangular, then the triangle is equilateral. Corollary to Theorem 4-4 If a triangle is equiangular, then the triangle is equilateral.                                       

Assignment Pg. 213 #1-2;7-16; 21-24