This section covers how figures compare when they are moved, resized or both. It has four lessons and a practice set, and belongs to the wider SPM Mathematics guide.
What does this section cover?
Start with recognising congruent figures, which shows what stays the same after a move. Then learn calculating enlargement scale factors, which shows what changes.
Next is finding the centre of enlargement. The last lesson is describing the order of combined transformations. The practice set mixes all four.
One triangle, four questions
Take a triangle with sides 3, 4 and 5 cm.
| Question | What it tests | Key idea |
|---|---|---|
| Is a triangle with sides 4, 3 and 5 cm congruent to it? | Congruency | Three equal sides, so yes (SSS) |
| It is enlarged so the 3 cm side becomes 9 cm. What is the scale factor? | Scale factor | 9 ÷ 3 = 3 |
| Two pairs of matching points are known. Where is the centre? | Centre of enlargement | Lines through matching points meet at the centre |
| It is translated and then reflected. Is the order important? | Combined transformations | Reversing the order can change the image |
The shape never changes. The question decides which skill applies.
Who should start where?
If congruent and similar figures still blur together, begin with congruency. If scale factors come out upside down, go to scale factors first.
If you can calculate but cannot locate the centre, use the centre of enlargement lesson. If combined transformations land in the wrong place, start with the order lesson.
For a teacher to go through your reasoning question by question, see online one-to-one Mathematics tuition.