Prove two triangles congruent

A standard method from Geometry and data basics: the steps and worked examples.

Steps

Name the triangles with matching vertices in the same order (△ABC ≅ △DEF).
List three pairs of equal parts, one per line, each with a reason (given, common side, vert. opp. ∠s, …).
State the condition: SSS, SAS, ASA, AAS or RHS.
Never use AAA or SSA. They do not prove congruence.

Example 1: Prove two triangles congruent: AB and CD cross at M, with AM = BM and CM = DM. Prove △AMC ≅ △BMD.

AM = BM            (given)
∠AMC = ∠BMD        (vert. opp. ∠s)
CM = DM            (given)
∴ △AMC ≅ △BMD      (SAS)

The angle is between the two sides in both triangles, so this is SAS, not SSA.

For the whole topic, read Geometry and data basics: key points, common mistakes and how the DSE tests it.