How to teach angles, polygons and enlargement
Year 7 to Year 9 (ages 12 to 15)
This strand covers naming angle relationships made by parallel lines and a transversal, finding a polygon's interior angle sum from its number of sides, classifying quadrilaterals by their properties, and enlarging a shape by a scale factor.
How to teach it
- Teach angles on a straight line (sum to 180) and at a point (sum to 360) first, since every other angle rule builds on these.
- Introduce corresponding and alternate angles as EQUAL pairs, and co-interior angles as a pair that adds to 180, using a labelled diagram every time.
- Derive the polygon angle-sum formula, (n - 2) x 180, by splitting a polygon into triangles from one vertex, rather than just stating it.
- Classify quadrilaterals (square, rectangle, rhombus, parallelogram, trapezium, kite) by their side and angle properties, not just their appearance.
- Teach enlargement as 'every length times the scale factor, every angle unchanged', using a scale factor greater than 1 before a fractional one.
Worked example
Find the sum of the interior angles of a hexagon (6 sides) (n - 2) x 180 = (6 - 2) x 180 = 4 x 180 = 720 degrees
Common mistakes
- Mixing up which angle pairs are equal (corresponding, alternate) versus which add to 180 (co-interior).
- Using the wrong value of n (number of sides) or forgetting to subtract 2 in the polygon angle-sum formula.
- Assuming a shape is a specific quadrilateral (e.g. a rhombus) from its appearance rather than checking its properties.
- Believing enlargement changes a shape's angles as well as its side lengths.
Frequently asked questions
What are corresponding, alternate and co-interior angles?
These describe angle pairs formed when a transversal crosses two parallel lines. Corresponding and alternate angles are always EQUAL; co-interior angles always ADD to 180 degrees.
How do you find the angle sum of a polygon?
The interior angles of any polygon with n sides add to (n - 2) x 180 degrees. A triangle (3 sides) sums to 180 degrees, a quadrilateral (4 sides) to 360 degrees, and so on.
What is an enlargement transformation?
An enlargement resizes a shape by a scale factor from a fixed centre point: every length is multiplied by the scale factor, while every angle stays exactly the same, so the shape keeps its proportions.
What year are angles, polygons and enlargement taught?
In the Australian Curriculum, angles on parallel lines and polygon angle sums are Year 7 skills (AC9M7M04-05), classifying polygons and 2D representation also start at Year 7 (AC9M7SP01-02), quadrilateral properties are Year 8 (AC9M8SP02), and enlargement is Year 9 (AC9M9SP02).
Practise with free worksheets
Printable worksheets with answer keys that are never wrong.