Prove that the angles at the base of an isosceles triangle are equal. Theorem: In an isosceles triangle, the angles at the base are equal.

Given:
triangle ABC – isosceles,
Prove that angle A = angle C.
Evidence:
Let’s draw the ВO bisector. Consider the ABO triangles and the BOC triangle.
Angle ABO = angle OBC because AO is bisector by construction.
The ВO side is common.
AB = BC by definition of an isosceles triangle.
Therefore, the ABO triangle = the BOC triangle on both sides and the angle between them. Then the angle A = angle C. That is what was required to prove.