Geometry — NSW Year 8 Maths
Unknown angles found by reasoning, from parallel lines to triangles, quadrilaterals and polygons. Seven subtopics and 140 practice questions, each with a fully worked solution, aligned to NESA outcomes MA4-ANG-C-01 and MA4-GEO-C-01.
Geometry in NSW Year 8
Geometry in Year 8 is about reasoning rather than measuring. Students take the angle facts met in Year 7, such as angles on a straight line, vertically opposite angles and the angles formed where a line crosses two parallel lines, and chain them together to find unknown angles, writing the reason beside every step. They also classify triangles and quadrilaterals from their sides, angles and diagonals.
The seven subtopics below start with angle chases and angles on parallel lines, then classify triangles and quadrilaterals and use the properties of each special quadrilateral as reasons. The last two cover the angle sums of triangles and quadrilaterals, then extend the idea to polygons with any number of sides, which looks ahead to Stage 5. Geometry is one of the 14 topics in NSW Year 8 Maths and belongs to the Measurement and Space strand (NESA outcomes MA4‑ANG‑C‑01 and MA4‑GEO‑C‑01). This kind of reasoning leads straight into Congruent Figures later in Year 8.
Subtopics
Geometry: common questions
What geometry do you learn in Year 8 maths?
You find unknown angles at a point, on straight lines and on parallel lines, classify triangles and quadrilaterals, use the properties of special quadrilaterals and their diagonals, and work with the angle sums of triangles, quadrilaterals and other polygons. Every step is written with a reason.
What are corresponding, alternate and co-interior angles?
They are pairs of angles made when a line crosses two parallel lines. Corresponding angles (an F shape) and alternate angles (a Z shape) are equal, while co-interior angles (a C shape) add to \(180^\circ\). So if \(x\) and \(115^\circ\) are co-interior, \(x = 65^\circ\).
How do you find the angle sum of a polygon?
Draw the diagonals from one vertex. They split a polygon with \(n\) sides into \(n - 2\) triangles, so its angles add to \((n - 2) \times 180^\circ\). A hexagon splits into 4 triangles, so its angles add to \(720^\circ\).
Which NESA outcomes cover geometry in Year 8?
Geometry sits in Stage 4 of the NSW Mathematics K–10 Syllabus (2022) under outcomes MA4‑ANG‑C‑01 (angle relationships, including parallel lines) and MA4‑GEO‑C‑01 (properties of triangles and quadrilaterals). The angle sum of any polygon goes a step further and is Stage 5 content in the syllabus.
What comes after geometry in Year 8?
The same reasoning is used in Congruent Figures, where students prove that two triangles are congruent and use this to explain the properties of quadrilaterals. In Stage 5 it extends to similar figures and more formal geometric proofs.