Geometry/Congruent Triangles

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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

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