Download Name:_________________________________ Date:________ Period:______ Isosceles Triangles

Name:_________________________________
Date:________ Period:______
Isosceles Triangles
Ms. Anderle
Isosceles Triangles
Remember: An isosceles triangle is a triangle that has __________ congruent sides.
Isosceles Triangle Theorems:

If two sides of a triangle are congruent, then the angles opposite those sides are
congruent. (Base angle of an isosceles triangle are congruent.)

If two angles of a triangle are congruent, then the sides opposite those angles are
congruent.
Proofs:
1.
Given: ΔABC is isosceles, with base AB
̅̅̅̅ ≅ ̅̅̅̅
𝐷𝐴
𝐸𝐵
Prove: ΔDAC ≅ ΔEBC
2.
⃡
Given: 𝐴𝐶
∢1 ≅ ∢4
Prove: ΔABC is isosceles
3.
Given: ⃡𝐷𝐸
∡1 ≅ ∡2
̅̅̅̅
̅̅̅̅ ≅ 𝐸𝐴
𝐷𝐵
Prove: ΔDCE is isosceles
4.
Given: ΔABC is isosceles
̅̅̅̅
̅̅̅̅ is the altitude to 𝐴𝐶
𝐵𝐷
Prove: ̅̅̅̅
𝐴𝐷 ≅ ̅̅̅̅
𝐶𝐷
5.
Given: ΔVIN is isosceles
̅̅̅
𝐼𝐷 is the altitude to ̅̅̅̅
𝑉𝑁
Prove: ∡𝑉𝐼𝐷 ≅ ∡𝑁𝐼𝐷
What do you notice about the altitude of an isosceles triangle?