Typically a triangle is presented with certain common or congruent sides and angles. Additional information may also be given (∠1 ≅∠2), (midpoints), (angle bisectors). The student is then asked to prove that the triangles are congruent using SSS, SAS, AAS or (ASA) congruency tests. This will typically require the student to use other KNOWN facts of triangles (complementary angles, exterior angles, sum of interior angles, etc) in order to prove that one of the Four congruency criteria are met.
Wyzant provides a examples of the two-column proofs that are typically used - look under Lessons (Geometry/Triangles)