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Pythagorean theorem worksheets

Every answer on these sheets is a whole number, and that is on purpose. These free printable worksheets build every triangle from a Pythagorean triple, so a child practices the theorem rather than a square root.

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Pythagorean theorem
Pythagorean theorem worksheet — Sides to 70 cm, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

Drawn from any two legs, the theorem almost never gives a whole hypotenuse, and a sheet built that way asks a thirteen-year-old for the square root of 41 in a blank the width of a number. Triples such as 3-4-5, 5-12-13, and 8-15-17, together with all their multiples, are what a textbook uses for the same reason: the arithmetic stays clean so the method can be the difficulty.

Why this sheet works

Finding a leg is a separate setting from finding the hypotenuse, and worth a whole sheet of its own. One is an addition then a square root; the other is a subtraction then a square root, and children who have only ever done the first will add when they should take away — reliably, and it is the mistake this standard is really about.

How this one works

Right triangle, 5 and 12

512?
  1. The hypotenuse is the side OPPOSITE the right angle — never one of the two that make the corner. It is also always the longest, so you can check yourself twice.
  2. Here the hypotenuse is the missing one, so the two given sides are both legs: 5 and 12.
  3. Square the two you have: 5² = 25 and 12² = 144.
  4. The two squares ADD to the square on the hypotenuse: 25 + 144 = 169.
  5. That is the square, not the side. Take the square root: √169 = 13 cm.

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