Isosceles and Equilateral Triangles Ch. 5-3 Geometry St. Barnabas HS Bronx, NY

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

Isosceles Triangle Theorem: If two sides of a triangle are congruent, the angles opposite these sides are congruent. Isosceles Triangle Theorem: Q V T E Z M G P D ) ) ) Corollary : The median from the vertex angle of an isosceles triangle bisects the vertex angle Corollary : The median from the vertex angle of an isosceles triangle is perpendicular to the base. ) x In other words: The median, altitude and angle bisector from the vertex of an isosceles triangle are all the same segment.

Equilateral Triangles Corollary : Every equilateral triangle is equiangular. A B C Or A B C Or A B C ) ) ) B C )

Ex: Isosceles Triangles If the following pairs of segments are congruent, which angles are congruent. F T D L K Q

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

Proofs w/Isosceles Triangles V D Proofs w/Isosceles Triangles 1) Given: Prove: M G x D H y T 2) Given: Prove: A Q E L P N 3) Given: Prove:

Algebra w/Isosceles Triangles