Triangle Congruence Criteria Geometry Definition. The steps below show the most general case for determining a congruence between two triangles that satisfy the sas criteria. 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.
This is one of them (hl). Two right triangles are congruent if the hypotenuse and one corresponding leg are equal in both triangles. Explain how the criteria for triangle congruence (asa, sas, and sss) follow from the definition of congruence in terms of rigid motions.
This criterion for triangle congruence is one of our axioms.
Common core (geometry) common core for mathematics. Two right triangles are congruent if the hypotenuse and one corresponding leg are equal in both triangles. Use triangle congruence criteria, rigid motions, and other properties of lines and angles to prove congruence between different triangles. 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).