1Geometry Lesson: Isosceles and Equilateral Triangle Theorems Aim: What theorems apply to isosceles and equilateral triangles? Do Now: C A K B Given: Prove: StatementsReasons 1) 2) 3) 4) 5) 6) Given Def. angle bisector Reflexive Postulate S.A.S. Postulate C.P.C.T.C.

2Geometry Lesson: Isosceles and Equilateral Triangle Theorems Isosceles Triangle Theorem: Theorem #8: ) ) ) ) Isosceles triangles ) ) Base angles of an isosceles triangle are congruent. Corollary #8-1: The bisector of the vertex angle of an isosceles triangle bisects the base. Corollary #8-2: The bisector of the vertex angle of an isosceles triangle is perpendicular to the base. Q V T E Z M G P D ) ) x In other words: The median, altitude and angle bisector from the vertex of an isosceles triangle are all the same segment.

3Geometry Lesson: Isosceles and Equilateral Triangle Theorems Equilateral Triangles A B C ) ) Or A B C ) ) A B C ) ) B C ) ) ) Corollary #8-3: Every equilateral triangle is equiangular.

4Geometry Lesson: Isosceles and Equilateral Triangle Theorems Ex: Isosceles Triangles FT D L K Q If the following pairs of segments are congruent, which angles are congruent.

5Geometry Lesson: Isosceles and Equilateral Triangle Theorems Ex: Proof w/Isosceles Triangle StatementsReasons 1) 2) 3) 4) 5) 6) 7) K M T R A V Given: Prove: Given Def. Of midpoint Given A.S.A. Postulate C.P.C.T.C

6Geometry Lesson: Isosceles and Equilateral Triangle Theorems Proofs w/Isosceles Triangles T R V D 1) Given: Prove: 2) Given: Prove: M G x D H y T A Q E L P N 3) Given: Prove:

7Geometry Lesson: Isosceles and Equilateral Triangle Theorems Algebra w/Isosceles Triangles