Pythagorean Theorem Practice

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Date:

📚 Part 1: Multiple Choice

1. Show your work for finding the hypotenuse of a right triangle with legs 3 and 4.

2. Which of these is a Pythagorean triple?

(3, 4, 5)

(2, 3, 4)

(5, 5, 7)

(6, 8, 10)

3. A ladder leans against a wall. The base is 3 ft from the wall and the ladder reaches 4 ft high. What is the length of the ladder?

4.5 ft

5 ft

5.5 ft

6 ft

4. Using side lengths 6, 8, and 10, what type of triangle is this?

Right triangle

Acute triangle

Obtuse triangle

Not a triangle

5. A right triangle has one leg measuring 8 cm and a hypotenuse of 10 cm. What is the length of the other leg?

6 cm

7 cm

8 cm

9 cm

6. A triangle has sides of lengths 9, 12, and 15. Is this a right triangle? Select Yes or No.

Yes

7. If a right triangle has a hypotenuse of 10 and one leg is 6, what is the other leg? Show your work.

8. Check if a triangle with sides 5, 12, and 13 is a right triangle. Explain your answer.

9. A ramp rises 2 ft and extends 3 ft horizontally. What is the length of the ramp? Show your calculation.

10. Find the hypotenuse for legs 5 and 12. Explain why the Pythagorean Theorem is used for right triangles.

11. A right triangle has legs measuring 7 m and 24 m. What is the length of the hypotenuse? Show your work.

12. A triangular park has sides of lengths 8 m, 15 m, and 17 m. Is it a right triangle? Justify your answer.