Chapter 4: Congruent Triangles

1. Chapter 4:Congruent Triangles Section 4-5: Isosceles and Equilateral Triangles

2. Objective • To use and apply properties of isosceles triangles.

3. Vocabulary • Legs of an isosceles triangle • Base of an isosceles triangle • Vertex angle of an isosceles triangle • Base angles of an isosceles triangle • corollary

4. Isosceles Triangles • Recall: an isosceles triangle is a triangle with at least two congruent sides. • Parts of an isosceles triangle: • The congruent sides of an isosceles triangle are the legs. • The third side is the base. • The two congruent sides form the vertex angle. • The other two angles are the base angles.

5. Theorem 4-3:“Isosceles Triangle Theorem” • If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

6. Theorem 4-4:“Converse of Isosceles Triangle Theorem” • If two angles of a triangle are congruent, then the sides opposite the angles are congruent.

7. Theorem 4-5 • The bisector of the vertex angle is the perpendicular bisector of the base.

8. Find the value of y

9. Corollary • A corollary is a statement that follows immediately from a theorem.

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

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