1. 4.5 - Isosceles and Equilateral Triangles

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

3. Theorem 4-3 Isosceles Triangle Theorem If two sides of a triangle are congruent, then the angles opposite those sides are congruent. AB C  A   B

4. Statements Reasons AB C Given: AC  BC Prove:  A   B (hint: draw an angle bisector for  C)

5. Theorem 4-4 Converse of the Isosceles Triangle Theorem If two angles of a triangle are congruent, then the sides opposite the angles are congruent. AC  BC AB C

6. Theorem 4-5 The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base. CD  AB and CD bisects AB AB C D

7. A corollary is a statement that follows immediately from a theorem. Corollary to Theorem 4-3 If a triangle is equilateral, then the triangle is equiangular. X Y Z  X   Y   Z

8. Corollary to Theorem 4-4 If a triangle is equiangular, then the triangle is equilateral. XY  YZ  ZX X Y Z

9. Find the values of the variables.

11. Complete each statement.

12. Find the measure of each angle.

13. Homework p. 213 2 - 17, 21 - 26