Congruence Conditions for Triangles
Grade 6The four conditions
Two triangles are congruent if they are exactly the same shape and size. There are four valid conditions — proving any one of them is enough.
SSS: all three sides equal. SAS: two sides and the included angle equal. ASA (or AAS): two angles and a corresponding side equal. RHS: right angle, hypotenuse, and one side equal.
SSA (two sides and a non-included angle) is not a valid congruence condition — two different triangles can share those measurements. Never use SSA as a proof.
Proving congruence in a question
State each pair of equal sides or angles, give the reason for each one, then name the congruence condition used. That structure earns all three marks.
Worked example
EXAMPLE
Triangles ABC and PQR have AB = PQ, BC = QR, and angle ABC = angle PQR. Are the triangles congruent? If so, state the condition.
AB = PQ (given). BC = QR (given). Angle ABC = angle PQR (given). These are two sides and the included angle. Therefore the triangles are congruent by SAS (side-angle-side).
