Year 9 - Maths
Further demonstrating of Pythagoras' theorem
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 there is a relationship between the lengths of the sides of a right-angled triangle.
Key Notes
- A visual approach can help you understand the structure behind Pythagoras' theorem.
- There is a difference between proof and demonstration.
- A demonstration would be showing Pythagoras' theorem works for specific right-angled triangles.
- A proof is generalised i.e. using four congruent triangles arranged in a particular way inside a square.
- The sum of the squares of the two shorter sides equals the square of the longest side.
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).
Common Mistakes To Avoid
- Pythagoras' theorem is just a relationship between the three sides of 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.
A visual approach can help you understand the structure behind Pythagoras' theorem. There is a difference between proof and demonstration.
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: Pythagoras' theorem is just a relationship between the three sides of a right-angled triangle. Correction: Whilst this is true, Pythagoras' theorem can more visually be represented as three squares whose sides are equal in length to the three sides of the triangle. The sum of the areas of the two smaller squares is equal to the area of the larger square.
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
- 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.