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Pythagorean Theorem Practice Tests

These Grade 8 Math practice tests cover right triangles, missing side lengths, square roots, exact radical answers, coordinate distance, the converse of the theorem, and real-world applications.

Skills covered

  • Using \(a^2+b^2=c^2\) to find a missing side
  • Identifying the hypotenuse and checking right triangles
  • Simplifying square roots and exact radical expressions
  • Applying the distance formula on the coordinate plane
  • Classifying triangles and solving ramp, ladder, diagonal, and travel problems

How to use these practice tests

Label the hypotenuse first, substitute the known lengths, solve for the missing side, and check that the hypotenuse is the longest side. Keep exact radical forms when a decimal is not requested.

For more Grade 8 Math practice, return to the Grade 8 Math category.

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Grade 8 Pythagorean Theorem Practice Tests

Practice Grade 8 Math questions about the Pythagorean Theorem, right triangles, square roots, distance, the converse, and real-world applications.

Choose the best answer for each question. Identify the hypotenuse, use the Pythagorean Theorem, and simplify exact radical answers when needed.

10 Questions
0/10 Questions0 %
Correct 0
Incorrect 0
Unanswered 10
1. QuestionMultiple choice

What is the distance between (0,0)(0,0) and (3,4)(3,4)?

Please select an answer first.

Correct answer: A

The correct answer is 55.

  1. Identify the right triangle: Locate the right angle and label the hypotenuse as the side opposite that angle.
  2. Apply the theorem: The horizontal and vertical changes are 3 and 4, so d=sqrt32+42=5d=\\sqrt{3^2+4^2}=5.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

The horizontal and vertical changes are 3 and 4, so d=sqrt32+42=5d=\\sqrt{3^2+4^2}=5.

2. QuestionMultiple choice

What is the distance between (−1,2)(-1,2) and (5,10)(5,10)?

Please select an answer first.

Correct answer: B

The correct answer is 1010.

  1. Identify the right triangle: Locate the right angle and label the hypotenuse as the side opposite that angle.
  2. Apply the theorem: The changes are 6 and 8, so d=sqrt62+82=10d=\\sqrt{6^2+8^2}=10.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

The changes are 6 and 8, so d=sqrt62+82=10d=\\sqrt{6^2+8^2}=10.

3. QuestionMultiple choice

What is the distance between (2,3)(2,3) and (2,9)(2,9)?

Please select an answer first.

Correct answer: C

The correct answer is 66.

  1. Identify the right triangle: Locate the right angle and label the hypotenuse as the side opposite that angle.
  2. Apply the theorem: The points have the same x-coordinate, so the vertical distance is ∣9−3∣=6|9-3|=6.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

The points have the same x-coordinate, so the vertical distance is ∣9−3∣=6|9-3|=6.

4. QuestionMultiple choice

What is the distance between (−2,−1)(-2,-1) and (4,−1)(4,-1)?

Please select an answer first.

Correct answer: D

The correct answer is 66.

  1. Identify the right triangle: Locate the right angle and label the hypotenuse as the side opposite that angle.
  2. Apply the theorem: The points have the same y-coordinate, so the horizontal distance is ∣4−(−2)∣=6|4-(-2)|=6.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

The points have the same y-coordinate, so the horizontal distance is ∣4−(−2)∣=6|4-(-2)|=6.

5. QuestionMultiple choice

Which formula gives the distance between (x1,y1)(x_1,y_1) and (x2,y2)(x_2,y_2)?

Please select an answer first.

Correct answer: A

The correct answer is d=sqrt(x2−x1)2+(y2−y1)2d=\\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}.

  1. Identify the right triangle: Locate the right angle and label the hypotenuse as the side opposite that angle.
  2. Apply the theorem: The distance formula applies the Pythagorean Theorem to the horizontal and vertical changes.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

The distance formula applies the Pythagorean Theorem to the horizontal and vertical changes.

6. QuestionMultiple choice

What is the distance from the origin to (5,12)(5,12)?

Please select an answer first.

Correct answer: B

The correct answer is 1313.

  1. Identify the right triangle: Locate the right angle and label the hypotenuse as the side opposite that angle.
  2. Apply the theorem: Use d=sqrt52+122=sqrt169=13d=\\sqrt{5^2+12^2}=\\sqrt{169}=13.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

Use d=sqrt52+122=sqrt169=13d=\\sqrt{5^2+12^2}=\\sqrt{169}=13.

7. QuestionMultiple choice

A path goes 8 units horizontally and 15 units vertically. What is the direct distance?

Please select an answer first.

Correct answer: C

The correct answer is 1717 units.

  1. Identify the right triangle: Locate the right angle and label the hypotenuse as the side opposite that angle.
  2. Apply the theorem: The direct distance is sqrt82+152=sqrt289=17\\sqrt{8^2+15^2}=\\sqrt{289}=17.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

The direct distance is sqrt82+152=sqrt289=17\\sqrt{8^2+15^2}=\\sqrt{289}=17.

8. QuestionMultiple choice

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

Please select an answer first.

Correct answer: D

The correct answer is 55.

  1. Identify the right triangle: Locate the right angle and label the hypotenuse as the side opposite that angle.
  2. Apply the theorem: The changes are 3 and 4, so the distance is sqrt32+42=5\\sqrt{3^2+4^2}=5.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

The changes are 3 and 4, so the distance is sqrt32+42=5\\sqrt{3^2+4^2}=5.

9. QuestionMultiple choice

What is the hypotenuse of the right triangle with points (0,0),(0,6),(8,0)(0,0),(0,6),(8,0)?

Please select an answer first.

Correct answer: A

The correct answer is 1010.

  1. Identify the right triangle: Locate the right angle and label the hypotenuse as the side opposite that angle.
  2. Apply the theorem: The legs have lengths 6 and 8, so c=sqrt62+82=10c=\\sqrt{6^2+8^2}=10.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

The legs have lengths 6 and 8, so c=sqrt62+82=10c=\\sqrt{6^2+8^2}=10.

10. QuestionMultiple choice

What is the distance between (−3,4)(-3,4) and (1,1)(1,1)?

Please select an answer first.

Correct answer: B

The correct answer is 55.

  1. Identify the right triangle: Locate the right angle and label the hypotenuse as the side opposite that angle.
  2. Apply the theorem: The changes are 4 and -3; the distance is sqrt42+(−3)2=5\\sqrt{4^2+(-3)^2}=5.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

The changes are 4 and -3; the distance is sqrt42+(−3)2=5\\sqrt{4^2+(-3)^2}=5.

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