Year 9 - Maths
Checking understanding of similarity
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 enlarge a shape and can state what changes and what is invariant.
Key Notes
- An enlargement means a change in size.
- The lengths of the lines may change when enlarged.
- The angles inside an object do not change when enlarged.
- When an object is enlarged, the image is similar.
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.
- Scale factor: Scale factor is the multiplier between similar shapes that describes how large one shape is compared to the other.
- Invariant: A property of a shape is invariant if that property has not changed after the shape is transformed.
Common Mistakes To Avoid
- When a pair of similar shapes are not in the same orientation, pupils may select an incorrect pair of lengths to calculate the scale factor.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
An enlargement means a change in size. The lengths of the lines may change when enlarged.
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: When a pair of similar shapes are not in the same orientation, pupils may select an incorrect pair of lengths to calculate the scale factor. Correction: Encourage pupils to take a systematic approach to locating pairs of corresponding lengths by looking for the longest edge in each shape, then the second longest, third longest, etc.
More Lessons In This Unit
- Applying the criteria for congruence Study Guide
- Checking understanding of congruence 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
- Similarity in shapes Study Guide
Browse all guides in the Year 9 Maths guide library.