Properties of Geometric Figures — NSW Year 9 Advanced Maths
Angles in polygons, symmetry, transformations and networks. Eight subtopics and 160 practice questions with worked solutions, aligned to NESA outcomes MA4-GEO-C-01, MA5-GEO-P-01, MA5-LIN-P-01 and MA5-NET-P-01.
Properties of Geometric Figures in NSW Year 9 Advanced
Properties of Geometric Figures uses angle facts and reasoning to find unknown angles and to explain why results are true. In Year 9 Advanced, students revise triangle and quadrilateral properties, find the interior and exterior angle sums of any polygon, describe symmetry and transformations with coordinates, and meet networks and planar graphs.
The eight subtopics below cover triangle geometry, quadrilateral geometry, the angle sum of a polygon and its exterior angles, line and rotational symmetry, transformations on the number plane, networks, and planar graphs with Euler's formula. Properties of Geometric Figures is one of the 14 topics in NSW Year 9 Advanced Maths and belongs to NESA's Measurement and Space strand. It revises the Stage 4 outcome MA4‑GEO‑C‑01 and covers the Stage 5 Path outcomes MA5‑GEO‑P‑01, MA5‑LIN‑P‑01 and MA5‑NET‑P‑01. The reasoning here leads on to the congruence proofs later in the course.
Subtopics
Properties of Geometric Figures: common questions
What is the angle sum of a polygon?
A polygon with \(n\) sides has interior angles that add to \(180(n - 2)^\circ\). A hexagon has an angle sum of \(180 \times 4 = 720^\circ\), so each angle of a regular hexagon is \(120^\circ\).
What do the exterior angles of a polygon add to?
In any convex polygon, the exterior angles add to \(360^\circ\). Each exterior angle of a regular polygon with \(n\) sides is \(\frac{360^\circ}{n}\), so a regular polygon with exterior angles of \(18^\circ\) has 20 sides.
What is rotational symmetry?
A shape has rotational symmetry of order \(n\) if it fits onto itself \(n\) times in one full turn. A regular hexagon has order 6, and its smallest turn is \(60^\circ\).
What is Euler's formula for networks?
For a connected planar graph, \(v - e + f = 2\). Here \(v\) is the number of vertices, \(e\) the number of edges and \(f\) the number of faces, including the outside face. A graph with 10 edges and 5 faces has \(v = 2 + 10 - 5 = 7\) vertices.
Which NESA outcomes does this topic cover?
Triangles and quadrilaterals revise the Stage 4 outcome MA4‑GEO‑C‑01. Polygon angle sums use MA5‑GEO‑P‑01, symmetry and transformations use MA5‑LIN‑P‑01, and networks and planar graphs use MA5‑NET‑P‑01, all Stage 5 Path outcomes.