4-5 Isosceles & Equilateral Triangles M11.C.1 2.9.11.B

1. 4-5 Isosceles & Equilateral TrianglesM11.C.1 2.9.11.B Objectives: To use and apply properties of isosceles triangles

2. Vocab • Legs – congruent sides of an isosceles triangle. • Base – third side • Vertex Angle – two congruent sides form an angle • Base Angles – other two angles

3. Isosceles Triangle Theorem If two sides of a triangle are congruent, then the angle opposite those sides are congruent.

4. Converse of Isosceles Triangle Theorem Converse of Isosceles Triangle – If two angles of a triangle are congruent, then the sides opposite the angle are congruent.

5. Vocab • Triangle Bisector – the bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base.

6. Example • Suppose that you draw XB YZ. Can you use SAS to prove △XYB ≅△XZB? T

7. Explain why △ABC is isosceles

8. Explain why ∆RST is isosceles.

9. Example - Find x and y

10. Vocabulary • A corollary is a statement that follows immediately from a theorem.

11. 2 Corollarys • If a triangle is equilateral, then the triangle is equiangular. • If a triangle is equiangular, then the triangle is equilateral.

12. Class Work • Page 213 #3-16, 21-26