The Proof of the Isosceles Triangle Theorem

An isosceles triangle is a triangle whose two sides are congruent. In the figure below, $latex ABC$ is an isosceles triangle and $latex \overline{AB} \cong \overline{BC}$.

The Isosceles Triangle Theorem states that the angles opposite to the two congruent sides of an isosceles triangle are congruent. In the figure above, the theorem states that since $latex AB \cong BC$, $latex \angle A \cong \angle C$.

The proof to this theorem uses the SSS triangle congruence. The SSS Triangle Congruence Theorem states that if the three corresponding sides of two triangles are congruent, then the two triangles are congruent. Continue reading