Geometry/Congruent Triangles

Methods of Determining Congruence

Two triangles are congruent if:

• each pair of corresponding sides is congruent
• two pairs of corresponding angles are congruent and a pair of corresponding sides are congruent
• two pairs of corresponding sides and the angles included between them are congruent

Tips for Proofs

Commonly used prerequisite knowledge in determining the congruence of two triangles includes:

• by the reflexive property, a segment is congruent to itself
• vertical angles are congruent
• when parallel lines are cut by a transversal corresponding angles are congruent
• when parallel lines are cut by a transversal alternate interior angles are congruent
• midpoints and bisectors divide segments and angles into two congruent parts