1. 4-5 Isosceles and Equilateral Triangles

2. Isosceles Triangles The congruent sides of an isosceles triangle are its legs. The third side is the base. The legs form the vertex angle. The other two angles are the base angles.

3. Isosceles Triangle Theorems Isosceles Triangle Theorem: If two sides of a triangle are congruent, then the angles opposite those sides are congruent. (Also known as the Base Angles Theorem) Converse of the Isosceles Triangle Theorem: If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

4. Using the Isosceles Triangle Theorems Is AB congruent to CB? Explain. Is  A congruent to  DEA? Explain.

5.  Answer the following: Is  WVS congruent to  S? Explain. Is TR congruent to TS? Explain.

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

7. Using Algebra What is the value of x?  Suppose m  A = 27. What is the value of x?

8. Corollaries A corollary is a theorem that can be proved easily using another theorem. 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.

9. Finding Angle Measures What are the measures of  A,  B, and  ADC?