Year 9 - Maths
Determining which side
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 identify which side length is missing and use the appropriate form of Pythagoras' theorem to calculate it.
Key Notes
- The hypotenuse is the side opposite the right angle.
- It does not matter which of the shorter sides is identified as a or b.
Vocabulary To Learn
- right-angled triangle: A right-angled triangle has exactly one 90° interior angle.
- hypotenuse: A hypotenuse is the side of the right-angle triangle which is opposite the right-angle.
- Pythagoras' theorem: Pythagoras' theorem shows that the sum of the squares of the two shorter sides of a right-angled triangle is equal to the square of its longest side (the hypotenuse).
Common Mistakes To Avoid
- I can only use Pythagoras' theorem to find the length of a side of a right-angled triangle when the right-angle marker is labelled, so I know which side is the hypotenuse.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
The hypotenuse is the side opposite the right angle. It does not matter which of the shorter sides is identified as a or b.
2. Use this key word in a maths sentence and explain it clearly. 'right-angled triangle'
A right-angled triangle has exactly one 90° interior angle. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: I can only use Pythagoras' theorem to find the length of a side of a right-angled triangle when the right-angle marker is labelled, so I know which side is the hypotenuse. Correction: The right-angle marker doesn't need to be explicitly labelled in order to be able to identify the right-angle. You can use knowledge of "interior angles in a triangle sum to 180°" to find the right angle, given two other angles.
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
- Congruent, similar or neither Study Guide
- Demonstrating Pythagoras' theorem 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.