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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

Do side lengths 6, 8, and 10 form a right triangle?

Please select an answer first.

Correct answer: A

The correct answer is Yes.

  1. Identify the right triangle: Locate the right angle and label the hypotenuse as the side opposite that angle.
  2. Apply the theorem: Since 62+82=36+64=100=1026^2+8^2=36+64=100=10^2, the converse confirms a right triangle.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

Since 62+82=36+64=100=1026^2+8^2=36+64=100=10^2, the converse confirms a right triangle.

2. QuestionMultiple choice

Do side lengths 7, 8, and 10 form a right triangle?

Please select an answer first.

Correct answer: B

The correct answer is No.

  1. Identify the right triangle: Locate the right angle and label the hypotenuse as the side opposite that angle.
  2. Apply the theorem: The largest side is 10, but 72+82=1137^2+8^2=113, not 102=10010^2=100.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

The largest side is 10, but 72+82=1137^2+8^2=113, not 102=10010^2=100.

3. QuestionMultiple choice

Do side lengths 9, 40, and 41 form a right triangle?

Please select an answer first.

Correct answer: C

The correct answer is Yes.

  1. Identify the right triangle: Locate the right angle and label the hypotenuse as the side opposite that angle.
  2. Apply the theorem: The relationship 92+402=81+1600=1681=4129^2+40^2=81+1600=1681=41^2 holds.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

The relationship 92+402=81+1600=1681=4129^2+40^2=81+1600=1681=41^2 holds.

4. QuestionMultiple choice

What type of triangle has side lengths 5, 6, and 7?

Please select an answer first.

Correct answer: D

The correct answer is Acute.

  1. Identify the right triangle: Locate the right angle and label the hypotenuse as the side opposite that angle.
  2. Apply the theorem: For the largest side, 72=497^2=49 and 52+62=615^2+6^2=61; because 49 is smaller, the triangle is acute.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

For the largest side, 72=497^2=49 and 52+62=615^2+6^2=61; because 49 is smaller, the triangle is acute.

5. QuestionMultiple choice

If c2=a2+b2c^2=a^2+b^2 for the largest side c, what can be concluded?

Please select an answer first.

Correct answer: A

The correct answer is The triangle is a right triangle..

  1. Identify the right triangle: Locate the right angle and label the hypotenuse as the side opposite that angle.
  2. Apply the theorem: The converse of the Pythagorean Theorem says that this equality proves the angle opposite c is right.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

The converse of the Pythagorean Theorem says that this equality proves the angle opposite c is right.

6. QuestionMultiple choice

If the square of the largest side is greater than the sum of the squares of the other sides, the triangle is:

Please select an answer first.

Correct answer: B

The correct answer is Obtuse.

  1. Identify the right triangle: Locate the right angle and label the hypotenuse as the side opposite that angle.
  2. Apply the theorem: If c2>a2+b2c^2>a^2+b^2, the angle opposite c is obtuse.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

If c2>a2+b2c^2>a^2+b^2, the angle opposite c is obtuse.

7. QuestionMultiple choice

If the square of the largest side is less than the sum of the squares of the other sides, the triangle is:

Please select an answer first.

Correct answer: C

The correct answer is Acute.

  1. Identify the right triangle: Locate the right angle and label the hypotenuse as the side opposite that angle.
  2. Apply the theorem: If c2<a2+b2c^2<a^2+b^2, the angle opposite c is acute.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

If c2<a2+b2c^2<a^2+b^2, the angle opposite c is acute.

8. QuestionMultiple choice

Do side lengths 12, 16, and 20 form a right triangle?

Please select an answer first.

Correct answer: D

The correct answer is Yes.

  1. Identify the right triangle: Locate the right angle and label the hypotenuse as the side opposite that angle.
  2. Apply the theorem: Since 122+162=144+256=400=20212^2+16^2=144+256=400=20^2, the triangle is right.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

Since 122+162=144+256=400=20212^2+16^2=144+256=400=20^2, the triangle is right.

9. QuestionMultiple choice

What type of triangle has side lengths 4, 5, and 6?

Please select an answer first.

Correct answer: A

The correct answer is Acute.

  1. Identify the right triangle: Locate the right angle and label the hypotenuse as the side opposite that angle.
  2. Apply the theorem: The largest side gives 62=366^2=36, while 42+52=414^2+5^2=41; the smaller square means acute.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

The largest side gives 62=366^2=36, while 42+52=414^2+5^2=41; the smaller square means acute.

10. QuestionMultiple choice

What type of triangle has side lengths 5, 5, and 8?

Please select an answer first.

Correct answer: B

The correct answer is Obtuse.

  1. Identify the right triangle: Locate the right angle and label the hypotenuse as the side opposite that angle.
  2. Apply the theorem: The largest side gives 82=648^2=64, while 52+52=505^2+5^2=50; the larger square means obtuse.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

The largest side gives 82=648^2=64, while 52+52=505^2+5^2=50; the larger square means obtuse.

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