Year 9 - Maths
Congruence 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 for congruent shapes both side lengths and angle sizes are preserved.
Key Notes
- Two shapes are not congruent if there is a pair of lengths with a scalar not equal to one.
- Congruent does not mean the orientation must be the same.
- The angle sizes do not change.
Vocabulary To Learn
- Congruent: If one shape can fit exactly on top of another using rotation, reflection or translation, then the shapes are congruent.
- Co-interior angles: Co-interior angles are on the same side of the transversal line and in between the two other lines.
Common Mistakes To Avoid
- Pupils may think that they do not have enough information about a shape to determine whether it is congruent to another shape, when in fact they do.
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 congruent if there is a pair of lengths with a scalar not equal to one. Congruent does not mean the orientation must be the same.
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 think that they do not have enough information about a shape to determine whether it is congruent to another shape, when in fact they do. Correction: Pupils could attempt the draw the shape based on the information that they have. They can then consider whether there are multiple way that the shape can be drawn while still satisfying all the given information.
More Lessons In This Unit
- Applying the criteria for congruence Study Guide
- Checking understanding of congruence Study Guide
- Checking understanding of similarity 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.