Year 9 - Maths
Similarity in shapes
Geometrical properties: similarity and Pythagoras' theorem
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
This unit explores the concepts of congruence and similarity, and ways to prove or disprove similarity between shapes. We then explore further properties of triangles with Pythagoras' Theorem.
Lesson Summary
You will learn to recognise that similar shapes have sides in proportion to each other but angle sizes are preserved.
Key Notes
- Two shapes are not similar if there is a pair of lengths with a different multiplicative relationship.
- Similar shapes are not always easy to spot visually.
- A ratio table can help you find the scalar and functional multipliers in similar shapes.
- The angle sizes do not change.
Vocabulary To Learn
- Object: The object is the starting figure before a transformation has been applied.
- Image: The image is the resulting figure after a transformation has been applied.
- Similar: Two shapes are similar if the only difference between them is their size. Their side lengths are in the same proportions.
Common Mistakes To Avoid
- Pupils may find it difficult to match up corresponding measurements on two congruent shapes when they are in different orientations.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Two shapes are not similar if there is a pair of lengths with a different multiplicative relationship. Similar shapes are not always easy to spot visually.
2. Use this key word in a maths sentence and explain it clearly. 'Object'
The object is the starting figure before a transformation has been applied. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Pupils may find it difficult to match up corresponding measurements on two congruent shapes when they are in different orientations. Correction: Look lengths which are between any pairs of known angles or look for angles which are between pairs of adjacent known lengths. Also, tracing paper could be used to reflect/rotate/translate one shape onto the other.
More Lessons In This Unit
- Applying the criteria for congruence Study Guide
- Checking understanding of congruence Study Guide
- Checking understanding of similarity Study Guide
- Congruence in shapes Study Guide
- Congruent triangles (ASA and AAS) Study Guide
- Congruent triangles (RHS) Study Guide
- Congruent triangles (SAS) Study Guide
- Congruent triangles (SSS) Study Guide
- Congruent, similar or neither Study Guide
- Demonstrating Pythagoras' theorem Study Guide
- Determining which side Study Guide
- Further demonstrating of Pythagoras' theorem Study Guide
- Length of a shorter side Study Guide
- Length of the hypotenuse Study Guide
- Problem solving with similarity and Pythagoras' theorem Study Guide
- Pythagoras' theorem in context Study Guide
- Rotational symmetry Study Guide
Browse all guides in the Year 9 Maths guide library.