Pythagorean Theorem · Grades 8–8
Pythagorean Theorem Worksheets
a² + b² = c². Worksheets for finding a missing side of a right triangle, sometimes a leg and sometimes the hypotenuse, so it never settles into a pattern.
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What it is
In a right triangle, the Pythagorean theorem relates the legs and the hypotenuse: a² + b² = c².
Why it matters
A TV's screen size is quoted on the diagonal, not the width or height — that number comes straight from a² + b² = c², the relationship that turns two straight measurements into a distance you never walked off directly.
How to do it
- Identify the two legs (a, b) and the hypotenuse (c, opposite the right angle).
- Square the known sides.
- Add or subtract, then take the square root to find the missing side.
- Is it a right triangle? Check whether the two short sides squared add up to the longest side squared.
Examples by level
- BeginnerFind the missing leg =Answer12
- IntermediateFind the missing leg =Answer9
- AdvancedFind the missing leg =Answer16
Examples are generated by the same engine as the worksheets, so they're always mathematically correct. Built to avoid repeats, not reshuffle the same handful of questions.
Common mistakes
- Treating a leg as the hypotenuse.
- Forgetting to take the square root.
- Adding when you should subtract to find a leg.
Tips
- The hypotenuse is always the longest side.
- It only works for right triangles.
- In a word problem, sketch the triangle first: a ladder, a wall and the ground make a right angle.
For parents
The hypotenuse is always the longest side, opposite the right angle.
For teachers
Use Pythagorean triples (3-4-5, 5-12-13) so answers stay whole while the method is learned.
Key vocabulary
- hypotenuse
- the side opposite the right angle
- leg
- a side forming the right angle
Frequently asked questions
- What is the Pythagorean theorem?
- In a right triangle, a² + b² = c², where c is the hypotenuse.
- How do you find the hypotenuse?
- Square both legs, add them, then take the square root.
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