Pythagorean theorem worksheet
Forty questions on the Pythagorean theorem: the hypotenuse, a missing leg, right triangle or not, decimals, distance between points and word problems.
Download the free pythagorean theorem worksheet (PDF)
Pythagorean theorem worksheet
What’s on the worksheet
- 40 questions on pythagorean theorem, sized for US Letter paper
- 2 pages of questions plus an answer key on the last page
- Written for grade 8, matching Common Core 8.G.B.6, 8.G.B.7, 8.G.B.8
- Name and date lines at the top, and room to show the work
Sample questions from this worksheet
- Find the hypotenuse (legs 9 cm and 12 cm).
- Find the missing shorter side (hypotenuse 13 m, leg 5 m).
- Are 6, 8 and 10 the sides of a right triangle?
- Legs 3 and 5: hypotenuse to one decimal place ≈
- Distance from (1, 2) to (4, 6):
- A 13 ft ladder leans on a wall, its foot 5 ft from the wall. How high does it reach?
Preview the worksheet and answer key
Practice the Pythagorean theorem online
Between worksheets, a few minutes of online practice keeps the skill fresh. The Pythagorean theorem practice draws a right triangle with one side hidden, with a new triangle every time and the working shown after a wrong answer. The Pythagorean theorem lesson has a quiz and the squares-on-the-sides picture.
Make a new pythagorean theorem worksheet
Need another page for extra practice, a retake or a second group in class? The free Mathify Kids test maker builds a fresh pythagorean theorem worksheet with different numbers every time. Choose how many questions, print it with its own answer key, or let your child take it on screen and see the score straight away.
Pythagorean theorem: a worked example (A right triangle with legs 9 cm and 12 cm)
- Square the legs: 9² = 81 and 12² = 144.
- Add them: 81 + 144 = 225.
- Take the square root: √225 = 15.
- The hypotenuse is 15 cm. It is the longest side, which checks out.
How to use it at home and in class
At home
Ask your child to point to the hypotenuse first on every picture: it is opposite the right angle and always the longest side. A list of squares from 1² to 30² makes the square roots quicker. For Part D, a quick sketch of the right triangle between the two points helps. The Pythagorean theorem lesson shows the squares on each side. Ten problems a day works better than a whole sheet at once. Mark them together with the answer key, then ask your child to explain one they got wrong: finding the mistake themselves is where the learning happens.
In class
Use the first row as a warm-up, a full page for independent practice, or five questions as an exit ticket. For a retake or a second group, make a new version with the test maker so every child gets different numbers.
Mistakes to watch for
- Adding when the hypotenuse is given and a leg is missing.
- Forgetting the square root at the end.
- Using the theorem on a triangle that has no right angle.
- Adding the sides before squaring: (9 + 12)² is not 9² + 12².
What to practice before and after pythagorean theorem
- Before: volume of cones and spheres. If this sheet is a struggle, go back a step.
- Learn it first: the pythagorean theorem lesson.
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Questions parents ask
When do you add and when do you subtract in the Pythagorean theorem?
Add the squares to find the hypotenuse, the longest side. Subtract the square of the known leg from the square of the hypotenuse to find a shorter side.
What grade is this pythagorean theorem worksheet for?
It is written for grade 8 and matches Common Core standards 8.G.B.6, 8.G.B.7, 8.G.B.8.
Can I get a different version of this pythagorean theorem worksheet?
Yes. Use the free Mathify Kids test maker to make a new pythagorean theorem worksheet with different numbers every time. You choose how many questions, and every version comes with its own answer key.