Triangle congruence: SSS, SAS, ASA, RHS

OCR J560 Higher (J560/04, /06) tests congruence proofs. Foundation tests recognition. Each test is a fixed criterion — quote the test by its initialism.

The four congruence tests

SSS (Side-Side-Side)

All three pairs of sides equal.

• Triangles ABC and DEF: if AB = DE, BC = EF, CA = FD, then ΔABC ≡ ΔDEF.

SAS (Side-Angle-Side)

Two pairs of sides equal AND the included angle equal.

• The angle MUST be between the two equal sides.

ASA (Angle-Side-Angle)

Two pairs of angles equal AND a corresponding side equal.

• Note: AAS works too (the third angle is forced) but OCR uses ASA convention.

RHS (Right-Hypotenuse-Side)

Both triangles right-angled, hypotenuses equal, one other pair of sides equal.

NOT a test: SSA

Two sides and a non-included angle DO NOT generally determine a unique triangle ("ambiguous case"). So SSA is not a congruence criterion.

Congruence proofs — the format

OCR mark schemes look for:

1. State the equal pairs of sides/angles (with reasons: given, common side, vertically opposite, alternate angles, etc.).
2. Identify the test (SSS, SAS, ASA, RHS).
3. State the conclusion: triangles are congruent.

Marks distribute as: B1 for each correct identification of an equal pair, M1 for naming the correct test, A1 for the conclusion.

OCR mark scheme conventions

• Specific phrasing required: "common side" (not "shared"); "vertically opposite angles" (not just "opposite").
• Test must be named (SSS, SAS, ASA, RHS).
• For the angles in SAS, the marker MUST see the word "included" or the angle clearly between the two sides.