Year 9 - Maths
Checking understanding of congruence
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 translate, reflect and rotate a shape.
Key Notes
- Translation, reflection and rotation produce an image congruent to the object.
- Translation involves moving the shape.
- Rotation involves turning the shape about a defined point.
- Reflection involves flipping the shape.
Vocabulary To Learn
- Congruent: If one shape can fit exactly on top of another using rotation, reflection or translation, then the shapes are congruent.
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.
Translation, reflection and rotation produce an image congruent to the object. Translation involves moving the shape.
2. Use this key word in a maths sentence and explain it clearly. 'Congruent'
If one shape can fit exactly on top of another using rotation, reflection or translation, then the shapes are congruent. 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 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
- Similarity in shapes Study Guide
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