Year 10 - Maths
Checking and securing understanding of congruence and similarity
Further transformations
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit pupils apply their knowledge of transformations to explore negative enlargement factors and the application of multiple transformations.
Lesson Summary
You will learn to identify (by eye) which shapes are congruent, similar or neither.
Key Notes
- If two shapes are congruent, then they are similar.
- A ratio table can be a helpful tool for checking the multipliers.
- The multiplicative relationship between the sides of the object is preserved in its image.
- It can be easier to determine (by eye) which shapes are NOT congruent or similar.
Vocabulary To Learn
- Similar: Two shapes are similar if the only difference between them is their size. Their side lengths are in the same proportions.
- Congruent: If one shape can fit exactly on top of another using rotation, reflection or translation, then the shapes are congruent.
- 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.
- Invariant: A property of a shape is invariant if that property has not changed after the shape is transformed.
Common Mistakes To Avoid
- Congruent shapes are not similar shapes.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
If two shapes are congruent, then they are similar. A ratio table can be a helpful tool for checking the multipliers.
2. Use this key word in a maths sentence and explain it clearly. 'Similar'
Two shapes are similar if the only difference between them is their size. Their side lengths are in the same proportions. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Congruent shapes are not similar shapes. Correction: Congruent shapes are similar shapes. The scale factor, or multiplier, between them is one.
More Lessons In This Unit
- Advanced problem solving with further transformations Study Guide
- Checking and securing understanding of enlargement with positive fractional scale factors Study Guide
- Checking and securing understanding of enlargement with positive integer scale factors Study Guide
- Checking and securing understanding of reflection Study Guide
- Checking and securing understanding of rotation Study Guide
- Checking and securing understanding of translation Study Guide
- Describing a negative enlargement Study Guide
- Enlargement using a negative scale factor Study Guide
- Identifying multiple transformations Study Guide
- Multiple transformations Study Guide
- Problem solving with further transformations Study Guide
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