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Triangle Congruence Criteria Geometry Definition. Triangles are congruent if any pair of corresponding sides and their included angles are equal in both triangles. There are five ways to test that two triangles are congruent.

Given two triangles and so that (side), ∠ = ∠ (angle), and (side). There are criteria that refer to a few parts of the two triangles and a correspondence between them that guarantee congruency (i.e., existence of rigid motion). More formally, two sets of points are called congruent if, and only if, one can be transformed into the other by an isometry, i.e., a combination of rigid motions, namely a translation, a rotation, and a reflection.

Then the triangles are congruent.

If abc is a triangle, then it is denoted as ∆abc, where a, b and c are the vertices of the triangle. Two right triangles are congruent if the hypotenuse and one corresponding leg are equal in both triangles. Learn geometry congruence postulates with free interactive flashcards. Many resources like assessment examples, teaching notes, vocabulary lists, student worksheets, videos explanations, textbook connections, web links are all here to help teachers and students. So we do not prove it but use it to prove other criteria. There are criteria that refer to a few parts of the two triangles and a correspondence between them that guarantee congruency (i.e., existence of rigid motion).