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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10 questions — 4 Foundation, 4 Standard, 2 Extension — with full worked solutions, calibrated to the Victorian Curriculum.
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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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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