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Mathematics chapter guide

Congruency, enlargement and combined transformations

Moving, shrinking and growing shapes feel like separate topics until you see what stays the same.

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.

Common questions

What do congruency and enlargement have in common?

Both compare an original figure with an image. Congruent figures have the same shape and size. An enlargement keeps the shape but changes the size by a scale factor, so the figures are similar, not congruent.

Which skill should I study first?

Start with recognising congruent figures, because it shows what a transformation keeps. Then learn scale factors, then how to find a centre of enlargement, and finish with the order of combined transformations.

Why does the order of transformations matter?

A combined transformation applies one transformation and then another to the result. Reversing the order can give an image in a different position, so the notation must be read carefully.

Do I need to draw every diagram?

A quick sketch on a grid helps you check your answer. Coordinates also help, because you can test a rule on one point before applying it to a whole shape.

If transformation questions make sense in class but fall apart on a new diagram, one-to-one Mathematics lessons let a teacher watch where your reading of the figure goes wrong and fix that step.

  • Online one-to-one lessons for your child with an experienced teacher.
  • Your first class is a one-hour trial, from RM50. The fee is agreed before you book.
  • Happy with the teacher? Continue with lessons of about 1.5 hours. If not, ask for another teacher.