Pythagorean Theorem and Geometry Quiz

Grade 9 · Math · Quiz

Test your skills applying the Pythagorean Theorem to find missing sides and solve geometry problems.

Questions

1. A right triangle has legs of 5 and 12. What is the hypotenuse?

   1. 13
   2. 15
   3. 17
   4. 11
   Show answer

   Answer: 13

   c² = 25 + 144 = 169; c = 13.

2. The set (6, 8, 10) is a Pythagorean triple.

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   Answer: True

   6² + 8² = 36 + 64 = 100 = 10². ✓

3. What is the distance between (1, 1) and (4, 5)?

   1. 4
   2. 5
   3. 6
   4. 7
   Show answer

   Answer: 5

   d = √((4−1)² + (5−1)²) = √(9 + 16) = √25 = 5.

4. A right triangle has hypotenuse 25 and one leg 7. The other leg is ___.

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   Answer: 24

   b² = 25² − 7² = 625 − 49 = 576; b = 24.

5. Which set of numbers is NOT a Pythagorean triple?

   1. (3, 4, 5)
   2. (5, 12, 13)
   3. (6, 8, 9)
   4. (8, 15, 17)
   Show answer

   Answer: (6, 8, 9)

   6² + 8² = 100 ≠ 81 = 9². Not a triple.

6. The Pythagorean Theorem only applies to right triangles.

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   Answer: True

   The Pythagorean Theorem requires a right angle to hold.

7. If a = 9 and c = 15 in a right triangle, what is b?

   1. 10
   2. 12
   3. 14
   4. 6
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   Answer: 12

   b² = 15² − 9² = 225 − 81 = 144; b = 12.

8. The hypotenuse of a right triangle with legs 1 and 1 is √___.

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   Answer: 2

   c² = 1² + 1² = 2; c = √2.

9. A ladder 10 m long leans against a wall with its base 6 m from the wall. How high does it reach?

   1. 7 m
   2. 8 m
   3. 9 m
   4. 6 m
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   Answer: 8 m

   h² = 10² − 6² = 100 − 36 = 64; h = 8 m.

10. The converse of the Pythagorean Theorem states that if a² + b² = c², the triangle is:

    1. Equilateral
    2. Isosceles
    3. Right
    4. Obtuse
    Show answer

    Answer: Right

    The converse confirms the triangle is right if a² + b² = c².

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