Pythagorean Theorem Quiz

Grade 8 · Math · Quiz

Test your ability to apply the Pythagorean Theorem to find missing side lengths in right triangles.

Questions

  1. The Pythagorean Theorem states that for a right triangle with legs a and b and hypotenuse c:

    1. a + b = c
    2. a² + b² = c²
    3. a² − b² = c²
    4. a × b = c²
    Show answer

    Answer: a² + b² = c²

    The Pythagorean Theorem is a² + b² = c², where c is the hypotenuse and a, b are the two legs.

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

    1. 5 cm
    2. 7 cm
    3. 6 cm
    4. 8 cm
    Show answer

    Answer: 5 cm

    3² + 4² = 9 + 16 = 25. √25 = 5. The 3-4-5 triangle is the most common Pythagorean triple.

  3. The hypotenuse is always the longest side of a right triangle.

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    Answer: True

    The hypotenuse is opposite the 90° angle, making it always the longest side in a right triangle.

  4. A ladder 10 m long leans against a wall. The base is 6 m from the wall. How high does the ladder reach?

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

    6² + h² = 10². 36 + h² = 100. h² = 64. h = 8 m.

  5. Which set of numbers is a Pythagorean triple?

    1. 2, 3, 4
    2. 5, 12, 13
    3. 4, 5, 6
    4. 3, 5, 7
    Show answer

    Answer: 5, 12, 13

    5² + 12² = 25 + 144 = 169 = 13². The set 5, 12, 13 satisfies a² + b² = c².

  6. In a right triangle, the side opposite the right angle is called the ___.

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    Answer: hypotenuse

    The hypotenuse is defined as the side across from the right angle — always the longest side.

  7. A right triangle has a hypotenuse of 13 and one leg of 5. What is the length of the other leg?

    1. 10
    2. 12
    3. 8
    4. 11
    Show answer

    Answer: 12

    5² + b² = 13². 25 + b² = 169. b² = 144. b = 12.

  8. The Pythagorean Theorem can be applied to any triangle, not just right triangles.

    Show answer

    Answer: False

    The Pythagorean Theorem only works for right triangles (those with a 90° angle).

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