4-5 Isosceles and Equilateral Triangles

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?