Year 9 - Maths
Length of a shorter 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 use Pythagoras' theorem to find the length of one of the shorter sides.
Key Notes
- The sum of the squares of the two shorter sides equals the square of the longest side.
- The difference between the squares of the longest and known shorter sides is the square of the remaining side.
- A calculator can perform these calculations efficiently.
- Rounding gives a less accurate answer so there might be times you wish to leave your answer with an operator.
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-angled 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
- The method for finding the length of a shorter side of a right-angled triangle using Pythagoras' theorem is exactly the same as when finding the hypotenuse.
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 difference between the squares of the longest and known shorter sides is the square of the remaining side.
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: The method for finding the length of a shorter side of a right-angled triangle using Pythagoras' theorem is exactly the same as when finding the hypotenuse. Correction: Whilst the initial setup of "the sum of the squares of the two shorter sides equals the square of the hypotenuse" will be the same, finding the length of a shorter side will require an extra step of rearranging terms in the equation.
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 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.