Pythagorean Theorem Worksheets

How to use the worksheet generator

1. Pick a problem type. Hypotenuse and missing-leg problems come with a labeled triangle drawn in one of 16 orientations, so students cannot rely on the hypotenuse always sitting in the same place. Mixed combines the two, which forces the key decision: add the squares or subtract them? Converse lists three side lengths to classify as acute, right or obtuse, Word problems leave room to sketch, and Distance plots two points on a grid.
2. Pick the numbers. Whole numbers builds every problem from Pythagorean triples, so all answers are exact. Radicals uses whole-number sides whose answers need simplest radical form, such as √80 = 4√5. Decimals uses lengths with one decimal place, rounded to the tenth or hundredth you choose.
3. Choose 6 to 20 problems, then press New worksheet until you like the set.
4. Print. The problems print first, under a line for name, date and score, and the answer key starts on a new page. Untick Print the answer key to print student copies only.

Printable worksheets with answer keys

The ready-made worksheets use hand-picked problems that build from easy to hard, with teacher notes and an answer key that shows every step. Every answer on them has been checked by computer.

For boxes and space diagonals, continue with the 3D Pythagorean theorem worksheet. Students who prefer instant feedback can use the Pythagorean theorem quiz or the practice problems with hidden solutions.

Which worksheet should students start with?

In the Common Core, the Pythagorean theorem belongs to 8th grade (standards 8.G.B.6 to 8.G.B.8), and high school geometry returns to it. This order follows the way most courses build the skill:

1. Hypotenuse, whole numbers. One operation, exact answers, confidence first.
2. Missing leg, then mixed. The new idea is subtraction, and mixed sheets check that students choose correctly.
3. Radicals. Once √50 = 5√2 is familiar, switch the generator to Radicals.
4. Word problems. The arithmetic is the same; the skill is drawing the triangle.
5. Converse. Run the theorem backward to test for a right angle.
6. Distance formula. The theorem on a coordinate grid, which leads to the equation of a circle.

Tips for teachers

• Ask for a label before any arithmetic. Students who write "hyp" or "leg" next to the unknown make far fewer add-versus-subtract errors.
• Watch for the four classic mistakes: squaring the sum (a + b)² instead of adding squares, adding when a leg is missing, forgetting the final square root, and putting the longest side in the a or b slot. The common mistakes page shows each one with a fix.
• Decide on exact or decimal answers in advance. Exact radicals reward algebra skills; decimals suit measurement contexts. The Radicals setting asks for both, which makes grading flexible.
• Use the key for feedback. Each solution shows the substitution, the squares and the root, so students can find the exact line where their work went wrong.
• Build a lesson around it. The lesson plan and classroom activities pair well with these sheets, and the teaching guide collects everything for teachers in one place.

Printing and saving as a PDF

Press Print worksheet or your browser's print shortcut. Menus, buttons and these notes are hidden when printing, so the page holds only the title, the name line, the problems and, on a new page, the answer key. To get a Pythagorean theorem worksheet as a PDF, choose Save as PDF as the printer in the print dialog. Turning off the browser's headers and footers in the same dialog gives a cleaner page.

Frequently asked questions

Are these Pythagorean theorem worksheets free?

Yes. The generator and every ready-made worksheet are free to use and print, with no account or sign-up. Make as many versions as your class needs.

Where is the answer key?

On screen it sits directly below the problems. When you print, it starts on a separate page so you can hand out the problems without it. On generated sheets you can also untick the answer-key box so it does not print at all.

How do I make different versions of the same worksheet?

Keep the settings and change the seed. Each seed gives a different set of problems at the same difficulty, which is useful for retakes or for neighboring desks. Note each seed, or bookmark the page address, to rebuild any version and its key later.

What grade learns the Pythagorean theorem?

In schools that follow the Common Core it is taught in 8th grade, including the converse and the distance between two points. High school geometry and trigonometry then build on it, for example in the distance formula and the special right triangles.

Should students round their answers?

Only when the problem says so. An answer like √45 is exact and should be simplified to 3√5; its decimal 6.71 is an approximation. Word problems usually call for a rounded decimal with units, because measurements are never exact anyway.