Properties of Geometric Figures — NSW Year 9 Core Maths
Angle facts in triangles and quadrilaterals: angle sums, exterior angles and the special quadrilaterals. Two subtopics and 40 practice questions, each with a fully worked solution, aligned to NESA outcome MA4-GEO-C-01.
Properties of Geometric Figures in NSW Year 9
This topic revises the angle properties of triangles and quadrilaterals: a triangle's angles add to \(180^\circ\), a quadrilateral's add to \(360^\circ\), and the special quadrilaterals have their own rules about sides, angles and diagonals.
The two subtopics below are triangle geometry and quadrilateral geometry. Properties of Geometric Figures is one of the 13 topics in NSW Year 9 Core Maths. The triangle and quadrilateral work revises the Stage 4 outcome MA4‑GEO‑C‑01 from the Measurement and Space strand. Angle reasoning leads to similar figures later in Year 9. Networks are studied in the Advanced courses.
Subtopics
Properties of Geometric Figures: common questions
How many degrees are in a triangle and a quadrilateral?
The angles of a triangle add to \(180^\circ\) and the angles of a quadrilateral add to \(360^\circ\). A quadrilateral's sum follows because a diagonal splits it into two triangles, and \(2 \times 180^\circ = 360^\circ\).
What is the exterior angle of a triangle?
It is the angle between one side and the extension of the next side. It equals the two interior angles at the other vertices added together, so an exterior angle of \(130^\circ\) with one opposite angle of \(45^\circ\) leaves \(85^\circ\) for the other.
How do you find the angles in an isosceles triangle?
The two angles opposite the equal sides are equal. If the angle between the equal sides is \(40^\circ\), the other two angles share \(180^\circ - 40^\circ = 140^\circ\), so each one is \(70^\circ\).
What are the properties of a parallelogram?
Opposite sides are parallel and equal, opposite angles are equal, and the diagonals bisect each other. Angles next to each other add to \(180^\circ\), so if one angle is \(65^\circ\), the angle beside it is \(115^\circ\).
Which NESA outcomes cover Properties of Geometric Figures in Year 9?
The triangle and quadrilateral angle work revises the Stage 4 outcome MA4‑GEO‑C‑01.