Using Pythagoras Worksheets, Grade 8 (8.G.B.7) – Free PDF + Answer Key

First page of the using pythagoras practice worksheet

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PDFs print on US Letter paper. Free for classroom and home use.

Watch: The Pythagorean Theorem Explained (a² + b² = c²)

Key idea

Hypotenuse missing ⇒ add. Leg missing ⇒ subtract. Then take the square root. A leg can never be longer than the hypotenuse — check it. For distance, the legs are the differences of the coordinates.

Sample problems

Legs 9 and 12. Find the hypotenuse.
Hypotenuse 17, one leg 8. Find the other leg.
Hypotenuse 10, one leg 6. Find the other leg, then check it against the hypotenuse.
Legs 2 and 3. Give the hypotenuse squared, and say why that is the exact answer.

Common mistakes to watch for

Answered 100, stopping at c squared. Writing “c² = 100” on its own line makes the missing root visible.
Added, getting 674 and about 26 — which is longer than the hypotenuse, so the check catches it immediately.
Said he added instead of subtracting, which is true and is not what the question asks. The question asks how he could TELL, and the answer is the comparison with the hypotenuse — a check he can run himself on any problem of this kind.

The answer key explains each one, so you can tell what a wrong answer means.

How to use this set

Teach with the slides (about 15 minutes), or watch the video together.
Practice with the worksheet. Questions climb from fluency to application to reasoning.
Check understanding with the exit ticket, and send the homework home.
Mark with the answer key — each answer shows the steps and the most likely mistake.