GCSE Maths: Similarity and Congruence Guide

Congruent shapes

Congruent shapes are exactly the same size and shape — one could be placed exactly on top of the other after only moving, rotating or reflecting it.

Proving congruence

Triangles can be proved congruent using SSS (all three sides equal), SAS (two sides and the included angle equal), ASA (two angles and the included side equal), or RHS (right angle, hypotenuse and one side equal).

Similar shapes

Similar shapes have the same shape but different sizes — corresponding angles are equal, and corresponding sides are all in the same ratio (scale factor).

Working with scale factors

If the length scale factor between two similar shapes is k, the area scale factor is k², and the volume scale factor is k³.

Common mistakes

• Confusing similar (same shape, different size) with congruent (identical).
• Forgetting to square or cube the scale factor for area and volume.
• Matching up the wrong corresponding sides or angles between two similar shapes.