Similarity
Similar shapes have the same angles and proportional sides, so one is an enlargement of the other.
▶ Interact
Play with the controls to see the idea in action.
📘 Learn
Similar shapes have the same angles and proportional sides, so one is an enlargement of the other.
- Scale factor links corresponding lengths
- Areas scale by the square of the factor
- Volumes scale by the cube
🧠 Quick quiz
Three questions. Score 2 or more to complete the topic.
What is Similarity?
Within Mathematics, which covers numbers, algebra, geometry, trigonometry and statistics from first principles to exam level, this topic explains Similarity. Maths builds step by step, so each topic here gives you a rule, a picture and a quick check you can use on homework and in exams.
Check that you can explain Similarity in your own words and give one example from everyday life. If you can do that, you have understood the core idea.
Understanding Similarity gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
Similarity in detail
Similar shapes have the same shape but different sizes: all corresponding angles are equal and all corresponding sides are in the same ratio, called the scale factor. A photograph and its enlargement are similar.
If the scale factor for lengths is k, then areas scale by k² and volumes by k³. Similar triangles let you find unknown lengths by setting up equal ratios, which is useful for finding heights of trees and buildings from shadows. Check that the sides you pair up truly correspond.
How the interactive helps you understand Similarity
Watch the shape transformation in the interactive. Use any sliders or buttons it offers to change the values and see how the shape transformation responds.
Before you change anything, predict the result. Then change one value at a time and check whether your prediction was right. This is a quick way to build a correct mental model of Similarity.
Real-life uses and examples
- Spot Similarity in exam questions, where it often sits inside a short word problem.
- Check a homework answer about Similarity by estimating first, then working it out step by step.
- Use Similarity when comparing prices, discounts or recipe quantities in everyday life.
Common mistakes to avoid
- Forgetting units, signs or brackets when you apply Similarity.
- Memorising the steps for Similarity without checking why they work.
- Learning the definition without testing it. Use the quiz and the interactive to check that you can apply the idea.
Frequently asked questions about Similarity
What is Similarity?
Similar shapes have the same angles and proportional sides, so one is an enlargement of the other.
What are the most important points about Similarity?
The main points are: Scale factor links corresponding lengths; Areas scale by the square of the factor; Volumes scale by the cube.
Why is Similarity useful?
Understanding Similarity gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
How can I practise Similarity?
Open the interactive at the top of this page and change the controls one at a time. Predict the result before each change, then take the three-question quiz. A score of two or more marks the topic as complete on this device.
Which topics are related to Similarity?
Related topics in Mathematics include Area of Trapezium and Parallelogram, Arcs and Sectors, Trigonometric Ratios.