Year 9 - Maths
Congruent, similar or neither
Geometrical properties: similarity and Pythagoras' theorem
Study Hub
Study Guides
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 differentiate between shapes which are congruent or similar or neither.
Key Notes
- If two shapes are congruent, then they are similar.
- Congruent shapes have a scalar of one.
- 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.
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.
Common Mistakes To Avoid
- Pupils may mix up the meanings of congruence and similarity or struggle with the hierarchy of their nested sets (e.g. thinking that all similar shapes are congruent rather than the other way around).
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. Congruent shapes have a scalar of one.
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: Pupils may mix up the meanings of congruence and similarity or struggle with the hierarchy of their nested sets (e.g. thinking that all similar shapes are congruent rather than the other way around). Correction: Frequently refer to a Venn diagram showing the set of congruence shapes inside the set of similar shapes when examining pairs of shapes.
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
- 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.