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All the triangles in the diagram above are similar – except one. Which triangle is the odd man out? Question 8 awaits your answer...

Similarity (F)

Learn similarity in GCSE Maths: compare shapes by equal angles and proportional sides, use scale factors, and link lengths, areas and volumes in diagrams and exam problems.

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Fascinating Fact:

In art scaling, perimeters scale like lengths. If k equals 4, perimeter new equals 4 × perimeter original. Edges all grow by the same factor.

In GCSE Maths, similarity means shapes keep the same angles while all lengths change by one scale factor. You’ll match corresponding sides, use ratios to find missing measures, and relate length, area, and volume.

Key Terms

Similar figures: Shapes with equal corresponding angles and sides in the same ratio.
Scale factor (k): The multiplier between matching lengths: k = (new length) ÷ (original length).
Corresponding sides: Matching sides that sit opposite equal angles in similar shapes.

Frequently Asked Questions (Click to see answers)

How do I find the scale factor between two similar shapes?

Choose matching sides and divide: k = (new length) ÷ (original length). Use the same pair each time; all other lengths then scale by k.

How do area and volume change for similar shapes?

Lengths scale by k, areas by k², and volumes by k³. Example: if k = 3, area scales by 9 and volume by 27.

How can I prove two triangles are similar in GCSE Maths?

Use angle–angle (AA), side–angle–side with proportional sides and the included angle equal (SAS), or side–side–side with all sides in the same ratio (SSS).