Congruence and Similar Figures — NSW Year 9 Advanced Maths
Congruence tests and proofs, similar figures, scale diagrams and similar triangles. Eight subtopics and 160 practice questions with worked solutions, aligned to NESA outcomes MA5-GEO-C-01, MA5-GEO-P-01 and MA5-GEO-P-02.
Congruence and Similar Figures in NSW Year 9 Advanced
Congruent figures are identical in shape and size, while similar figures have the same shape but may differ in size. In Year 9 Advanced, students use the congruence tests SSS, SAS, AAS and RHS to write formal proofs, use scale factors to find unknown lengths and areas in similar figures, work with scale drawings and maps, and test triangles for similarity.
The eight subtopics below cover congruent figures, tests for congruent triangles and congruent triangle proofs, then similar figures, properties of similar figures, scale diagrams, areas of similar figures and tests for similar triangles. Congruence and Similar Figures is one of the 14 topics in NSW Year 9 Advanced Maths and belongs to NESA's Measurement and Space strand (NESA outcomes MA5‑GEO‑C‑01, MA5‑GEO‑P‑01 and MA5‑GEO‑P‑02). Similar triangles explain why the trig ratios work, and the proofs prepare students for more formal geometry in Year 10 Advanced.
Subtopics
Congruence and Similar Figures: common questions
What are the four tests for congruent triangles?
SSS (three pairs of equal sides), SAS (two sides and the included angle), AAS (two angles and a matching side) and RHS (a right angle, the hypotenuse and one other side). Equal angles alone are not enough, because one triangle could be an enlargement of the other.
How do you find an unknown side in similar figures?
Find the scale factor from one pair of matching sides, then multiply or divide. If a 5 cm by 7 cm rectangle is enlarged so the 5 cm side becomes 15 cm, the scale factor is 3, so the 7 cm side becomes 21 cm.
How do the areas of similar figures compare?
If matching sides are in the ratio \(a : b\), the areas are in the ratio \(a^2 : b^2\). Circles with radii in the ratio \(2 : 3\) have areas in the ratio \(4 : 9\).
What does a map scale of 1 : 25 000 mean?
One unit on the map stands for 25 000 of the same unit on the ground. So 8.4 cm on the map is \(8.4 \times 25\,000 = 210\,000\) cm, or 2.1 km.
Which NESA outcomes cover congruence and similarity?
Similar figures and scale drawings are the Stage 5 Core outcome MA5‑GEO‑C‑01. Congruence tests, similarity tests and areas of similar figures are MA5‑GEO‑P‑01, and formal congruence proofs are MA5‑GEO‑P‑02, both Path outcomes.