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Pythagorean Theorem Quiz

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Pythagorean Theorem Quiz

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📘 Learning Goals & Supports

I can... use the Pythagorean Theorem to find a missing side of a right triangle and apply it to real-world problems.

Success criteria: I can identify legs and the hypotenuse, write a² + b² = c², substitute values correctly, and simplify to find the missing length (exact or rounded).

Differentiation strategies: Provide a calculator for arithmetic if needed; offer step-by-step templates and one worked example for students who need more support.

Extension: Find missing sides when lengths are decimals or use the theorem to verify whether three given lengths form a right triangle.

Dyslexia-friendly reading options: Read each problem aloud, use a ruler to track lines, and highlight numbers and keywords (leg, hypotenuse, diagonal).

📚 Part 1: Multiple Choice

1. A right triangle has legs of lengths 3 and 4. What is the length of the hypotenuse?

5

6

7

√13

2. If one leg of a right triangle is 5 and the hypotenuse is 13, what is the other leg?

12

8

√144

10

3. A ladder leans against a wall. The top reaches 15 ft high and the base is 8 ft from the wall. How long is the ladder (to the nearest foot)?

17 ft

23 ft

13 ft

20 ft

4. Which set of side lengths forms a right triangle?

6, 8, 11

7, 24, 25

5, 5, 5

9, 9, 18

✏️ Part 2: Short Answers & Matching

5. Find the missing leg. Hypotenuse = 10, one leg = 6. Show your work.
6. A rectangle is 9 in by 12 in. What is the length of its diagonal? Label units in your answer and show work.
7. Decide whether the triangle with sides 9, 40, 41 is a right triangle. Explain briefly.
8. The diagonal of a square street sign is 5 ft. What is the length of one side? Give an exact answer and a decimal to two decimal places.
9. Match each situation (left) with the correct action or result (right). Draw lines between matching items.
A. Find ladder length when height = 12 ft and base = 5 ft.
B. Verify if 8, 15, 17 form a right triangle.
C. Find diagonal of a 7 in by 24 in rectangle.
D. Side of square given diagonal 10√2 ft.
1. c² = a² + b² → c = 13 ft
2. Yes, because 8² + 15² = 17²
3. diagonal = √(7²+24²) = 25 in
4. side = 10 ft

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