Year 9 - Maths
Congruent triangles (RHS)
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 appreciate and use the criteria by which triangles are congruent (RHS).
Key Notes
- For a right-angled triangle, you need the hypotenuse and one other side length to prove congruence.
- Right-angled triangles, by definition, have a right-angle.
- There is a special relationship between the sides in a right-angled triangle.
Vocabulary To Learn
- Hypotenuse: The hypotenuse is the side of a right-angled triangle which is opposite the right angle.
Common Mistakes To Avoid
- Pupils may make assumptions about diagrams containing a right angle incorrectly.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
For a right-angled triangle, you need the hypotenuse and one other side length to prove congruence. Right-angled triangles, by definition, have a right-angle.
2. Use this key word in a maths sentence and explain it clearly. 'Hypotenuse'
The hypotenuse is the side of a right-angled triangle which is opposite the right angle. 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 make assumptions about diagrams containing a right angle incorrectly. Correction: Remind pupils, that they cannot assume there is a right angle, just because it may look like the two edges are perpendicular to each other.
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 (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.