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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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1. Test

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

A right triangle has legs 3 and 4. What is the hypotenuse?

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: Use c2=32+42=9+16=25c^2=3^2+4^2=9+16=25, so c=5c=5.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

Use c2=32+42=9+16=25c^2=3^2+4^2=9+16=25, so c=5c=5.

2. QuestionMultiple choice

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

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 c=sqrt52+122=sqrt25+144=sqrt169=13c=\\sqrt{5^2+12^2}=\\sqrt{25+144}=\\sqrt{169}=13.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

Use c=sqrt52+122=sqrt25+144=sqrt169=13c=\\sqrt{5^2+12^2}=\\sqrt{25+144}=\\sqrt{169}=13.

3. QuestionMultiple choice

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

Please select an answer first.

Correct answer: C

The correct answer is 1212.

  1. Identify the right triangle: Locate the right angle and label the hypotenuse as the side opposite that angle.
  2. Apply the theorem: Use b=sqrt132−52=sqrt169−25=sqrt144=12b=\\sqrt{13^2-5^2}=\\sqrt{169-25}=\\sqrt{144}=12.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

Use b=sqrt132−52=sqrt169−25=sqrt144=12b=\\sqrt{13^2-5^2}=\\sqrt{169-25}=\\sqrt{144}=12.

4. QuestionMultiple choice

A right triangle has legs 8 and 15. What is the hypotenuse?

Please select an answer first.

Correct answer: D

The correct answer is 1717.

  1. Identify the right triangle: Locate the right angle and label the hypotenuse as the side opposite that angle.
  2. Apply the theorem: Use c=sqrt82+152=sqrt64+225=sqrt289=17c=\\sqrt{8^2+15^2}=\\sqrt{64+225}=\\sqrt{289}=17.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

Use c=sqrt82+152=sqrt64+225=sqrt289=17c=\\sqrt{8^2+15^2}=\\sqrt{64+225}=\\sqrt{289}=17.

5. QuestionMultiple choice

What is the area of a right triangle with legs 6 and 8?

Please select an answer first.

Correct answer: A

The correct answer is 2424 square 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 area is frac12(6)(8)=24\\frac{1}{2}(6)(8)=24 square units.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

The area is frac12(6)(8)=24\\frac{1}{2}(6)(8)=24 square units.

6. QuestionMultiple choice

Which side of a right triangle is the hypotenuse?

Please select an answer first.

Correct answer: B

The correct answer is The side opposite the right angle.

  1. Identify the right triangle: Locate the right angle and label the hypotenuse as the side opposite that angle.
  2. Apply the theorem: The hypotenuse is always opposite the 90-degree angle and is the longest side.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

The hypotenuse is always opposite the 90-degree angle and is the longest side.

7. QuestionMultiple choice

A right triangle has legs 7 and 24. What is the hypotenuse?

Please select an answer first.

Correct answer: C

The correct answer is 2525.

  1. Identify the right triangle: Locate the right angle and label the hypotenuse as the side opposite that angle.
  2. Apply the theorem: Use c=sqrt72+242=sqrt49+576=sqrt625=25c=\\sqrt{7^2+24^2}=\\sqrt{49+576}=\\sqrt{625}=25.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

Use c=sqrt72+242=sqrt49+576=sqrt625=25c=\\sqrt{7^2+24^2}=\\sqrt{49+576}=\\sqrt{625}=25.

8. QuestionMultiple choice

A right triangle has hypotenuse 10 and one leg 6. What is the other leg?

Please select an answer first.

Correct answer: D

The correct answer is 88.

  1. Identify the right triangle: Locate the right angle and label the hypotenuse as the side opposite that angle.
  2. Apply the theorem: Use b=sqrt102−62=sqrt100−36=sqrt64=8b=\\sqrt{10^2-6^2}=\\sqrt{100-36}=\\sqrt{64}=8.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

Use b=sqrt102−62=sqrt100−36=sqrt64=8b=\\sqrt{10^2-6^2}=\\sqrt{100-36}=\\sqrt{64}=8.

9. QuestionMultiple choice

Which equation is the Pythagorean Theorem for legs a and b and hypotenuse c?

Please select an answer first.

Correct answer: A

The correct answer is c2=a2+b2c^2=a^2+b^2.

  1. Identify the right triangle: Locate the right angle and label the hypotenuse as the side opposite that angle.
  2. Apply the theorem: For a right triangle, the square of the hypotenuse equals the sum of the squares of the legs.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

For a right triangle, the square of the hypotenuse equals the sum of the squares of the legs.

10. QuestionMultiple choice

Do side lengths 9, 12, and 15 form a right triangle?

Please select an answer first.

Correct answer: B

The correct answer is Yes, because 92+122=1529^2+12^2=15^2.

  1. Identify the right triangle: Locate the right angle and label the hypotenuse as the side opposite that angle.
  2. Apply the theorem: The largest side is 15, and 92+122=81+144=225=1529^2+12^2=81+144=225=15^2.
  3. Check the length: Verify that the result is positive and that the hypotenuse is longer than either leg.

The largest side is 15, and 92+122=81+144=225=1529^2+12^2=81+144=225=15^2.

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