Congruent Triangle Proof

A congruence proof lists three matching facts, each with a reason, then names the test and draws a conclusion. This NSW Year 8 maths subtopic introduces formal proof, which the NSW syllabus places in Stage 5, using angle facts and triangle properties from Stage 4.

You will give reasons such as common side, vertically opposite angles, alternate angles on parallel lines, a midpoint and equal radii of a circle, fill the gaps in Line, Statement and Reason tables, and find the error in a proof that relies on SSA or lists the vertices in the wrong order. Skate ramps, fence posts with bracing wires and a chord in a circle turn the proofs into real problems. It is part of Year 8 Congruent Figures.