Year 8 - Pythagoras' theorem - Free practice
Year 8 Pythagoras' Theorem Worksheets
Find the hypotenuse, find a shorter side, apply to word problems.
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Six questions across Foundation, Standard and Extension, with full worked solutions, calibrated to the Victorian Curriculum.
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About this worksheet
Why we built it
Pythagoras' theorem is one of the most-tested Year 8 topics. These worksheets give your student practice across the three standard question types - finding the hypotenuse, finding a shorter side, and applying Pythagoras to real-world problems like ladders, ramps and TV screen sizes.
What's covered
Sub-skills your student will practise
- ✓Finding the hypotenuse given two shorter sides
- ✓Finding a shorter side given the hypotenuse
- ✓Identifying when a triangle is right-angled from its side lengths
- ✓Applied problems (ladders, ramps, diagonal distances)
- ✓Exact (surd) vs decimal answers
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From our families
Parents on the practice questions.
“Tuterly has been exactly what we needed since Tom started secondary school. Once the topic tests began, he was struggling to keep up. Now he has unlimited practice, all matched to what his class is actually covering, and his Maths results have improved noticeably.”
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Year 8 · Maths
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Year 9 · Maths
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Year 10 · Maths
Frequently asked
Questions parents ask about pythagoras' theorem
What is Pythagoras' theorem in plain English?
In a right-angled triangle, the square of the longest side (the hypotenuse) equals the sum of the squares of the other two sides. Written as a^2 + b^2 = c^2 where c is the hypotenuse.
How do students find a shorter side, not the hypotenuse?
Rearrange the formula: if c^2 = a^2 + b^2, then a^2 = c^2 - b^2. The shorter side equals the square root of the difference of squares, not the sum.
When does Pythagoras work?
Only in right-angled triangles. If the triangle has no 90-degree angle, Pythagoras doesn't apply - you'd need trigonometry or the cosine rule (Year 9-10 topics).
What real-world problems use Pythagoras?
Ladder problems (how tall a wall can a ladder reach), TV screen sizes (diagonal measurement), ramp gradients, and the distance between two points on a map. Year 8 introduces these contexts so the abstract formula has somewhere to land.
Want a real plan for the term?
Worksheets are great for repetition. A Tuterly tutor can spot the specific moves your student keeps getting wrong and fix them in one or two sessions.
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