If two sides of a triangle are congruent, then the angles opposite these sides are also congruent

Given

Isosceles triangle ABC, AB = AC

Prove
 

 Proof

1: AB = AC  -  Given
2: Draw angle bisector AO from A to BC
3: -  The bisector of the vertex angle of an isosceles triangle separates the triangle into two congruent triangles

4: -  CPCTC (Corresponding parts of congruent triangles are congruent)

The bisector of the vertex angle of an isosceles triangle separates the triangle into two congruent triangles

 Bisector of the vertex angle of an isosceles triangle

Given
Isosceles triangle ABC with AB = AC
AO bisects ,


Prove


Proof

1: AB=AC - Given
2: - Given

3: AO = AO - Identity

- From 1,2,3 - If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the triangles are congruent (SAS)

Isosceles Triangle

Isosceles Triangle

Isosceles Triangle hasTwo equal sides.
By the isosceles triangle theorem, the two angles opposite the equal sides are themselves equal