Congruence of Triangles

• Congruent triangles — same shape AND same size; one fits exactly over the other.
• CPCT — Corresponding Parts of Congruent Triangles are equal.
• Four congruence criteria: SSS, SAS, ASA, RHS.
• When two triangles are congruent, all 6 parts (3 sides + 3 angles) are equal.

Congruence criteria

AAA is NOT a congruence criterion — triangles can be same shape (similar) but different size. SSA is NOT a congruence criterion — ambiguous case.

CPCT

Once triangles are proved congruent, we can state: ∠A = ∠D, ∠B = ∠E, ∠C = ∠F and AB = DE, BC = EF, AC = DF (corresponding parts).

△ABC and △PQR: AB = PQ = 5 cm, BC = QR = 7 cm, ∠B = ∠Q = 60°. Are they congruent?

Given: AB = PQ (side), ∠B = ∠Q (included angle), BC = QR (side).
Criterion: SAS → △ABC ≅ △PQR by SAS.
By CPCT: AC = PR and ∠A = ∠P, ∠C = ∠R.

• Name the four congruence criteria.
• Why is AAA not a congruence criterion?
• Two right triangles have hypotenuse = 13 cm and one leg = 5 cm each. Are they congruent? Which criterion?
• What does CPCT stand for and when can we use it?

Open the Practice tab for graded questions on Congruence of Triangles.