Year 9 - Maths
Length of the hypotenuse
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 use Pythagoras' theorem to find the length of the hypotenuse.
Key Notes
- The sum of the squares of the two shorter sides equals the square of the longest side.
- The longest side is always opposite the right angle.
- A calculator can perform these calculations efficiently.
- Priority of operations makes the order clear.
Vocabulary To Learn
- 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).
- hypotenuse: A hypotenuse is the side of the right-angled triangle which is opposite the right-angle.
- right-angled triangle: A right-angled triangle has exactly one 90° interior angle.
Common Mistakes To Avoid
- Pythagorean triples can be a trio of any rational numbers that, when constructed into a triangle, always produces a right-angled triangle.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
The sum of the squares of the two shorter sides equals the square of the longest side. The longest side is always opposite the right angle.
2. Use this key word in a maths sentence and explain it clearly. '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). Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Pythagorean triples can be a trio of any rational numbers that, when constructed into a triangle, always produces a right-angled triangle. Correction: Pythagorean triples are conventionally a trio of integer side lengths of a right-angled triangle, such as the 3, 4, 5 triangle. Other, similar triangles can be generated from Pythagorean triples, whose side lengths are rational, such as 0.3, 0.4, 0.5.
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
- Determining which side Study Guide
- Further demonstrating of Pythagoras' theorem Study Guide
- Length of a shorter side 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.