Pythagorean Theorem Worksheets

Pythagorean theorem worksheets teach one of the most famous results in geometry: in a right triangle, a² + b² = c². These free printable Pythagorean theorem worksheets cover finding the hypotenuse, finding a missing leg, testing whether a triangle is right, and word problems, with an answer key on every PDF and a maker for new problems.

Quick answer: The Pythagorean theorem says that in a right triangle the square of the hypotenuse equals the sum of the squares of the legs: a² + b² = c². For legs 3 and 4, c = √25 = 5. This page has 7 free Pythagorean theorem worksheets (PDF) with answer keys for grade 8, plus a maker. Updated October 2026.

Ready-to-print samples

A few of the ready PDFs on this page. The full list is under Ready-to-print worksheets, and the maker above makes new problems on demand.

The Pythagorean theorem in three steps

1. Identify the hypotenuse c: the longest side, opposite the right angle.
2. Write a² + b² = c² and substitute the two sides you know.
3. Solve for the missing side by adding or subtracting the squares and taking the square root.

Pythagorean triples

Some right triangles have whole-number sides. These sets are called Pythagorean triples, and recognizing them speeds up many problems:

Pythagorean theorem worksheet: finding the hypotenuse

Square both legs, add, and take the square root. Answers that are not perfect squares can be left as a radical or rounded:

Find the missing side of a right triangle worksheet

When the hypotenuse is given, subtract the squares instead of adding them:

Converse of the Pythagorean theorem worksheet

The converse says that if a² + b² = c² for the three sides, the triangle has a right angle. Test the two shorter sides against the longest:

Try ten Pythagorean theorem problems

Use these as a warm-up. Draw the triangle first and label the hypotenuse.

Pythagorean theorem vocabulary

Students answer questions faster when they know the words. These are the terms used on the worksheets and answer keys:

Pythagorean theorem practice and word problems

This page is also searched as Pythagorean theorem practice, Pythagorean theorem problems, finding the hypotenuse worksheet and Pythagorean theorem word problems. All of them are the free PDFs above, with an answer key, for US Letter or A4, with no sign-up. The square root worksheets page covers the roots used to finish each problem.

How to use these Pythagorean theorem worksheets

Use the Pythagorean theorem worksheets in order. Start with the hypotenuse sheets until students can square and add without a calculator, then switch to the missing leg sheets, where the subtraction step is the new idea. Pythagorean theorem worksheets with a sketch work best, so ask students to draw and label every triangle.

Once the equation is automatic, use the Pythagorean theorem worksheets on right triangles and word problems for review. Print one of the Pythagorean theorem worksheets for homework, and use the answer key to check the work together the next day. Because every set can be regenerated, a student who needs more Pythagorean theorem worksheets can make a new one in seconds.

Common Core standards for the Pythagorean theorem

These worksheets practice the Common Core geometry standards for grade 8:

Common mistakes with the Pythagorean theorem

Real-life uses of the Pythagorean theorem

Builders, designers and navigators use right triangles daily:

Which Pythagorean theorem worksheet should you start with?

Start with the hypotenuse, then missing legs. Add the converse and word problems once the equation is automatic. Set B gives a retest for the first two levels.

A weekly plan for the Pythagorean theorem

More math practice

• Square root worksheets for the roots.
• Exponents worksheets for squares.
• The coordinate plane for the distance between two points.