Year 9 - Maths
Pythagoras' theorem in context
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 and apply Pythagoras' theorem to solve problems in a range of contexts.
Key Notes
- Within context, it can be difficult to initially identify whether Pythagoras' theorem can be used.
- Pythagoras' theorem may be used if a right-angled triangle can be drawn, even if drawn within a different shape.
- Pythagoras' theorem can be used to check for properties of other shapes involving right-angles.
Vocabulary To Learn
- perpendicular height: The perpendicular height is the perpendicular distance from the base to the opposite vertex.
- 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.
Common Mistakes To Avoid
- I need to be given a triangle in order to use Pythagoras' theorem.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Within context, it can be difficult to initially identify whether Pythagoras' theorem can be used. Pythagoras' theorem may be used if a right-angled triangle can be drawn, even if drawn within a different shape.
2. Use this key word in a maths sentence and explain it clearly. 'perpendicular height'
The perpendicular height is the perpendicular distance from the base to the opposite vertex. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: I need to be given a triangle in order to use Pythagoras' theorem. Correction: You do not need to be given a triangle. It is an important skill to be able to sketch and label a triangle for yourself from given information, or go straight into an algebraic stage of calculation if aware that lengths given are perpendicular.
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
- Length of the hypotenuse Study Guide
- Problem solving with similarity and Pythagoras' theorem Study Guide
- Rotational symmetry Study Guide
- Similarity in shapes Study Guide
Browse all guides in the Year 9 Maths guide library.