Congruent Figures — NSW Year 8 Maths
Same shape, same size: congruent figures, the four tests for congruent triangles, and short formal proofs about triangles and quadrilaterals. Four subtopics and 80 practice questions, each with a fully worked solution.
Congruent Figures in NSW Year 8
Two figures are congruent when one fits exactly on top of the other after a slide, flip or turn. In Year 8, students write congruence statements with the vertices in matching order, learn the four tests for congruent triangles (SSS, SAS, AAS and RHS), and use them to write short formal proofs.
The four subtopics below move from congruent figures to the tests, then to congruent triangle proofs and finally to proving the properties of parallelograms, rhombuses, rectangles and kites. Congruent Figures is one of the 14 topics in NSW Year 8 Maths and sits in the Measurement and Space strand. It goes beyond Stage 4: the NSW syllabus places congruence tests and proofs in Stage 5, so this topic builds on the Stage 4 properties of triangles and quadrilaterals and gives students a head start on similar figures and geometric proof.
Subtopics
Congruent Figures: common questions
What does congruent mean in Year 8 maths?
Congruent figures have the same shape and the same size, so every pair of matching sides and angles is equal. Translating, reflecting or rotating a figure keeps it congruent; enlarging it does not.
What are the four tests for congruent triangles?
SSS (three pairs of equal sides), SAS (two sides and the angle between them), AAS (two angles and a side in the same position) and RHS (a right angle, the hypotenuse and one other side). SSA and AAA are not tests.
How do you write a congruence statement?
Use the symbol \(\equiv\) and list the vertices in matching order. \(\triangle ABC \equiv \triangle PQR\) means A matches P, B matches Q and C matches R, so \(AB = PQ\) and \(\angle C = \angle R\).
Is congruence part of the NSW Stage 4 syllabus?
Not formally. The NSW Mathematics K–10 Syllabus (2022) places congruence tests and proofs in Stage 5, building on the Stage 4 properties of triangles and quadrilaterals. The Australian Curriculum includes congruence in Year 8, which is why it is part of this course.
How do you prove a property of a parallelogram?
Draw a diagonal to split it into two triangles, prove the triangles congruent using alternate angles and the common side, then read the property from the matching parts. This shows, for example, that a parallelogram’s opposite sides are equal.