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

2. 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

3. 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.

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

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

6. Ex: Proof w/Isosceles TriangleK 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

7. Proofs w/Isosceles TrianglesV 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:

8. Algebra w/Isosceles Triangles