Geometric Figures — NSW Year 10 Advanced Maths
Angle reasoning, congruent triangles, similar figures and similar triangles, with formal proofs. 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.
Geometric Figures in NSW Year 10 Advanced
Geometric Figures is about reasoning with shapes. Year 10 Advanced students find unknown angles and give a reason for every step, prove triangles congruent with the four tests, use scale factors to work with similar figures, including their areas and volumes, and prove triangles similar to find lengths that cannot be measured directly.
The four subtopics below start with basic geometry, then move to congruent triangles, similar figures and similar triangles. Geometric Figures is one of the 16 topics in NSW Year 10 Advanced Maths and sits within the Measurement and Space strand (NESA outcomes MA5‑GEO‑C‑01, MA5‑GEO‑P‑01 and MA5‑GEO‑P‑02). The proofs here prepare students for circle geometry and for Extension mathematics in Year 11.
Subtopics
Geometric Figures: common questions
What are the four tests for congruent triangles?
SSS (three pairs of equal sides), SAS (two pairs of equal sides and the included angle), AAS (two pairs of equal angles and a matching side) and RHS (right angle, hypotenuse and one other side).
What is the difference between congruent and similar?
Congruent figures are identical in shape and size. Similar figures have the same shape, so their angles are equal and their sides are in the same ratio, but they can be different sizes.
How do scale factors affect area and volume?
If lengths are multiplied by \(k\), areas are multiplied by \(k^2\) and volumes by \(k^3\). Two similar rabbits 10 cm and 16 cm tall have a length ratio of 1.6, so the larger uses \(1.6^3=4.096\) times as much chocolate: \(125\times4.096=512\) g.
How do you use similar triangles to find a height?
Find two triangles with matching angles, such as a child and their shadow from a spotlight, then use the same ratio of matching sides. If the sides are in the ratio 1 : 4, an unknown side is four times its partner.
Which NESA outcomes cover Geometric Figures?
Similar figures and scale factors are MA5‑GEO‑C‑01. The congruence and similarity tests, area and volume ratios, and angle reasoning are MA5‑GEO‑P‑01, and formal proofs are MA5‑GEO‑P‑02, in Stage 5 of the NSW Mathematics K–10 Syllabus (2022).