Congruence
Two shapes are congruent when they are identical in shape and size, even if rotated or reflected.
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Play with the controls to see the idea in action.
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Two shapes are congruent when they are identical in shape and size, even if rotated or reflected.
- Triangles are congruent by SSS, SAS, ASA or RHS
- Corresponding sides and angles are equal
- Proofs use these conditions
🧠 Quick quiz
Three questions. Score 2 or more to complete the topic.
What is Congruence?
Within Mathematics, which covers numbers, algebra, geometry, trigonometry and statistics from first principles to exam level, this topic explains Congruence. 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 Congruence in your own words and give one example from everyday life. If you can do that, you have understood the core idea.
Understanding Congruence gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
Congruence in detail
Two shapes are congruent if they are identical in shape and size, so one can be moved onto the other by translation, rotation or reflection. Matching sides and angles are equal.
To prove two triangles congruent you need one of four conditions: SSS (three sides equal), SAS (two sides and the included angle), ASA or AAS (two angles and a side) and RHS (right angle, hypotenuse and a side). Congruence proofs are used to show that lengths or angles are equal in geometric problems and underpin many theorems.
How the interactive helps you understand Congruence
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 Congruence.
Real-life uses and examples
- Spot Congruence in exam questions, where it often sits inside a short word problem.
- Check a homework answer about Congruence by estimating first, then working it out step by step.
- Use Congruence when comparing prices, discounts or recipe quantities in everyday life.
Common mistakes to avoid
- Forgetting units, signs or brackets when you apply Congruence.
- Memorising the steps for Congruence 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 Congruence
What is Congruence?
Two shapes are congruent when they are identical in shape and size, even if rotated or reflected.
What are the most important points about Congruence?
The main points are: Triangles are congruent by SSS, SAS, ASA or RHS; Corresponding sides and angles are equal; Proofs use these conditions.
Why is Congruence useful?
Understanding Congruence gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
How can I practise Congruence?
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 Congruence?
Related topics in Mathematics include Perimeter and Area, Area of a Circle, Pythagoras' Theorem.