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The Pythagorean Theorem unit pack (Grade 8 · CCSS 8.G.B.6, 8.G.B.7): every worksheet and exit ticket for this unit, ready to print in one go. The answer keys print at the end, each on its own page, so you can leave them off. To make a PDF, click Print and choose "Save as PDF." Games: Pythagorean Platforms

The Pythagorean Theorem

Grade 8 · CCSS 8.G.B.6, 8.G.B.7 · Pairs with the Pythagorean Platforms game
Name
Date
In a right triangle, a² + b² = c². Legs a and b make the right angle. The hypotenuse c is across from it, and it's always the longest side.
Steps: plug in → square → add (or subtract) → take the square root.

Key vocabulary

Part A: Find the hypotenuse (the rope)

1. a = 6 ft, b = 8 ft. Find c.
c = ft
2. a = 5 ft, b = 12 ft. Find c.
c = ft
3. a = 12 ft, b = 9 ft. Find c.
c = ft
4. a = 15 ft, b = 8 ft. Find c.
c = ft

Part B: Find the missing leg (the distance to the next platform)

5. c = 10 ft, b = 6 ft. Find a.
a = ft
6. c = 13 ft, b = 5 ft. Find a.
a = ft
7. c = 17 ft, a = 15 ft. Find b.
b = ft
8. c = 25 ft, a = 24 ft. Find b.
b = ft

Perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625

Part C: Word problems

9. An explorer's vine is tied to a branch 12 ft above her platform. The next platform is 16 ft straight across. How long must the vine be to reach it? Draw the triangle.
Answer: ft
10. A 15 ft rope hangs from an anchor 9 ft above a platform. How far across can the explorer swing to the next platform?
Answer: ft
11. A 13 ft ladder leans against a wall. Its base is 5 ft from the wall. How high up the wall does it reach?
Answer: ft
12. Find the mistake. Jordan found the hypotenuse of a triangle with legs 6 and 8 like this: c = 6 + 8 = 14. What did Jordan do wrong? Find the correct answer.
Correct c =
Play the game: studentmathgames.com/pythagorean-platforms© 2026 Mr. H · Free for classroom use

Exit Ticket: The Pythagorean Theorem

Grade 8 · CCSS 8.G.B.6, 8.G.B.7
Name
1. Find c.
c =
2. A 10 ft ladder leans on a wall with its base 6 ft out. How high does it reach?
ft
3. Is a triangle with sides 7, 24 and 25 a right triangle? Show how you know.
Yes / No

Answer Key: The Pythagorean Theorem

For the teacher
  1. 6² + 8² = 36 + 64 = 100, √100 → c = 10 ft
  2. 5² + 12² = 25 + 144 = 169, √169 → c = 13 ft
  3. 12² + 9² = 144 + 81 = 225, √225 → c = 15 ft
  4. 15² + 8² = 225 + 64 = 289, √289 → c = 17 ft
  5. a² + 6² = 10², a² = 100 − 36 = 64 → a = 8 ft
  6. a² + 5² = 13², a² = 169 − 25 = 144 → a = 12 ft
  7. 15² + b² = 17², b² = 289 − 225 = 64 → b = 8 ft
  8. 24² + b² = 25², b² = 625 − 576 = 49 → b = 7 ft
  9. Legs 12 and 16: 144 + 256 = 400, √400 → 20 ft
  10. Hypotenuse 15, leg 9: 225 − 81 = 144, √144 → 12 ft
  11. Hypotenuse 13, leg 5: 169 − 25 = 144, √144 → 12 ft
  12. Jordan added the side lengths instead of their squares. Correct: 6² + 8² = 100, √100 → c = 10. (14 can't be right: the hypotenuse has to be shorter than the two legs added together.)

Common mistakes to watch for: adding the sides (#12), doubling instead of squaring (6² = 12), stopping at c² without taking the square root, and adding instead of subtracting when finding a leg (Part B). The game's wrong answer choices are built from these same mistakes.

Full Teacher Guide: studentmathgames.com/pythagorean-platforms/guide© 2026 Mr. H

Answer Key: Exit Ticket

The Pythagorean Theorem
  1. 20² + 15² = 400 + 225 = 625, √625 → c = 25
  2. 6² + h² = 10², h² = 100 − 36 = 64 → 8 ft
  3. 7² + 24² = 49 + 576 = 625 = 25² → Yes (the converse of the Pythagorean theorem).

Quick read: a student who gets #1 but misses #2 is probably adding instead of subtracting when a leg is missing. Send them to World 4 of the game.