Tests for Congruent Triangles

Three well-chosen facts are enough to prove that two triangles are congruent. This NSW Year 8 maths subtopic teaches the four tests, SSS, SAS, AAS and RHS, which the NSW syllabus places in Stage 5, so it extends the Stage 4 work on triangles rather than matching a Stage 4 outcome.

You will name the test from the marks on a diagram, check that SAS uses the angle between the two sides and that RHS uses the hypotenuse, and see why SSA and AAA do not prove congruence. You will then use matching parts, a common side and vertically opposite angles to find unknown lengths and angles, including the support cables on a flagpole. It is part of Year 8 Congruent Figures.