Legs 5 and 12
Show answer
Hypotenuse 13
Free printable worksheet
Pythagorean Theorem Worksheet
Twelve right-triangle problems finding missing legs, hypotenuses, and real-world distances.
Middle School MathGrades 7-84 pagesAnswer key included
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What this worksheet includes
- Twelve right-triangle problems finding missing legs, hypotenuses, and real-world distances.
- 4-page printable PDF with a complete answer key
- Designed for Grades 7-8 middle school math practice
- Available as an immediate free download with no email required
How to use it
Use this pythagorean theorem worksheet for guided practice, independent review, homework, tutoring sessions, or a quick skills check. The spacious layout is designed to leave room for students to show their work rather than guess from crowded answer choices.
After students finish, compare their reasoning with the included answer key. When an answer is incorrect, have the student locate the first step where their work changed direction before trying the problem again.
Who this practice is for
This resource is designed for grades 7-8 students working on middle school math. Teachers, tutors, homeschool families, and parents can preview the first page before deciding whether the level and spacing fit the student.
Looking for a broader sequence? Browse all Middle School Math worksheets.
Topic guide
How to approach pythagorean theorem
For a right triangle, a² + b² = c² relates the two legs to the hypotenuse. The hypotenuse is opposite the right angle and is always the longest side.
Square the known side lengths before adding or subtracting, then take a square root. A diagram and a reasonableness check help prevent using a leg as c.
Learning objectives
- Identify legs and hypotenuse
- Find missing right-triangle sides
- Apply the theorem in context
Skills to review first
- Squares and square roots
- Solving one-step equations
- Right-triangle vocabulary
Worked example
Follow the reasoning step by step
Find the hypotenuse of a right triangle with legs 6 and 8.
- Use 6² + 8² = c².
- Compute 36 + 64 = 100.
- Take the principal square root of both sides.
- Check that the hypotenuse exceeds both legs.
Solution: c = 10.
Try before downloading
Three sample problems
Work each problem, then open the answer to check your result.
Hypotenuse 15 and leg 9
Show answer
Other leg 12
Do sides 8, 15, and 17 form a right triangle?
Show answer
Yes; 8² + 15² = 17².
Error check
Common mistakes to watch for
- Using the shorter side as c
- Adding when solving for a missing leg
- Forgetting to take the final square root