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Pythagorean Theorem Practice Test

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Pythagorean Theorem Practice Test

Right triangle illustration

📐 Part 1: Multiple Choice

Instructions: Choose the best answer for each question. Remember: a² + b² = c²

1. In a right triangle with legs of 3 and 4, what is the length of the hypotenuse?

5

7

25

12

2. Which set of numbers represents the sides of a right triangle?

2, 3, 4

5, 12, 13

1, 2, 3

4, 5, 6

3. A right triangle has a hypotenuse of 10 and one leg of 6. What is the other leg?

4

8

16

136

4. The Pythagorean theorem can be used with:

Right triangles only

Any triangle

Squares and rectangles

Circles

🔢 Part 2: Problem Solving

Instructions: Solve each problem. Show your work and round to the nearest tenth if necessary.

5. Find the missing side length:

Right triangle with legs a = 9 and b = 12. Find c.

6. Find the missing side length:

Right triangle with hypotenuse c = 17 and leg a = 8. Find b.

7. A ladder is leaning against a wall. The ladder is 25 feet long and the bottom is 7 feet from the wall. How high up the wall does the ladder reach?
8. A baseball diamond is a square with 90-foot sides. What is the distance from home plate to second base?

📝 Part 3: Applied Problems

9. A rectangular TV screen is 48 inches wide and 27 inches tall. What is the diagonal measurement of the screen?
10. Two cars leave an intersection at the same time. One travels north at 40 mph for 3 hours, the other travels east at 30 mph for 3 hours. How far apart are the cars after 3 hours?
11. True or False: A triangle with sides 15, 20, and 25 is a right triangle. Explain your answer.
12. A rectangular garden is 12 feet by 16 feet. What is the length of the diagonal path across the garden?

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