If two sides in a triangle are congruent, then the angles opposite them are congruent.
This theorem will be proven using congruent triangles.
has two congruent sides.
Draw the angle bisector that bisects and intersects at point
and share the following features.
For both triangles, two sides and the included angle are congruent. Thus,
according to the Side-Angle-Side Congruence Theorem. Because and are corresponding angles in congruent triangles, they are congruent. Therefore, if two sides in a triangle are congruent, the angles opposite them are congruent.
This can be summarized in a two-column proof.
|Draw an angle bisector,||Construction of angle bisector|
|Definition of angle bisector|
|Side-Angle-Side Congruence Theorem|
|Corresponding parts of congruent triangles are congruent|