Congruence and Similar Figures — NSW Year 9 Core Maths
Similar figures, scale factors, scale drawings and maps, and the tests for similar triangles. Four subtopics and 80 practice questions, each with a fully worked solution, aligned to NESA outcomes MA5-GEO-C-01 and MA5-GEO-P-01.
Congruence and Similar Figures in NSW Year 9
Congruent figures are identical in shape and size, while similar figures have the same shape but may differ in size, with every length multiplied by the same scale factor. In Year 9 Core this topic focuses on similarity: recognising similar figures, finding scale factors and unknown sides, reading maps and scale drawings, and proving that two triangles are similar before using them to find a length.
The four subtopics below cover similar figures, properties of similar figures, scale and scale factors, and tests for similar triangles. Congruence and Similar Figures is one of the 13 topics in NSW Year 9 Core Maths and belongs to the Measurement and Space strand. Similar figures, scale factors and scale drawings are Stage 5 Core content under NESA outcome MA5‑GEO‑C‑01, and the tests for similar triangles come from MA5‑GEO‑P‑01, which goes beyond the Core outcomes. Similar triangles also explain why the trigonometric ratios stay the same for a given angle, and lead to congruence proofs in later Stage 5 work.
Subtopics
Congruence and Similar Figures: common questions
What makes two figures similar?
Two figures are similar when their matching angles are equal and their matching sides are all in the same ratio. Triangles with sides \(6\), \(8\), \(10\) and \(9\), \(12\), \(15\) are similar, because every side has been multiplied by \(1.5\).
How do you find the scale factor?
Divide a length on the new figure by the matching length on the original. If a \(3\) cm side becomes \(12\) cm, the scale factor is \(12 \div 3 = 4\). A scale factor greater than \(1\) enlarges a figure and one less than \(1\) reduces it.
How do you use a map scale?
Multiply the map distance by the scale and convert the units. On a map with scale \(1 : 800\,000\), \(21\) cm on the map is \(21 \times 800\,000 = 16\,800\,000\) cm, which is \(168\) km.
What are the tests for similar triangles?
SSS: all three pairs of sides are in the same ratio. SAS: two pairs of sides are in the same ratio and the angles between them are equal. AA: two pairs of angles are equal. RHS: the hypotenuses and one other pair of sides of two right-angled triangles are in the same ratio.
Which NESA outcomes cover similar figures in Year 9?
Similar figures, scale factors and scale drawings are Stage 5 Core content under MA5‑GEO‑C‑01. The tests for similar triangles come from MA5‑GEO‑P‑01, which goes beyond the Core outcomes.