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

It's one of the most-used results in all of math, distance, construction, navigation, and coordinate geometry all rely on it.

How to do it

  1. Identify the two legs (a, b) and the hypotenuse (c, opposite the right angle).
  2. Square the known sides.
  3. Add or subtract, then take the square root to find the missing side.

Examples by level

  • Beginner
    34?
    Find the hypotenuse =5
  • Intermediate
    1160?
    Find the hypotenuse =61
  • Advanced
    112180?
    Find the hypotenuse =212

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.

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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