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Triangle Theorems Practice Tests

These Grade 10 Geometry practice tests develop theorem-based reasoning with triangle angles, side lengths, centers, inequalities, right-triangle formulas, and proof applications.

Skills covered

  • Applying the Triangle Sum, Exterior Angle, Isosceles, Larger Angle-Larger Side, and Triangle Inequality Theorems
  • Identifying medians, altitudes, angle bisectors, perpendicular bisectors, centroid, circumcenter, incenter, and orthocenter
  • Using the Pythagorean Theorem, its converse, geometric means, and 30-60-90 and 45-45-90 relationships
  • Solving side-length, angle-measure, perimeter, and exterior-angle problems
  • Using triangle theorems in congruence proofs, coordinate geometry, construction, and measurement applications

How to use these practice tests

Underline the givens and identify the theorem before calculating. For side-length questions, check the triangle inequality; for right triangles, label the hypotenuse before applying the formula.

For more Grade 10 Math practice, return to the Grade 10 Math category.

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Grade 10 Triangle Theorems Practice Tests

Practice Grade 10 Geometry questions about triangle angle and side theorems, centers, inequalities, right triangles, and proof applications.

Choose the best answer. Identify the relevant triangle theorem, substitute known measures, and check the result using a diagram, inequality, or algebraic relationship.

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

Which set of lengths can form a triangle?

Please select an answer first.

Correct answer: A

The correct answer is 5, 7, and 10..

  1. Identify the triangle information: List the angle measures, side lengths, center, segment, or proof relationship given in the problem.
  2. Apply the triangle theorem: Each pair of sides has a sum greater than the third: 5 + 7 > 10, 5 + 10 > 7, and 7 + 10 > 5.
  3. Check the conclusion: The correct answer is 5, 7, and 10..

Each pair of sides has a sum greater than the third: 5 + 7 > 10, 5 + 10 > 7, and 7 + 10 > 5.

2. QuestionMultiple choice

Which set of lengths cannot form a triangle?

Please select an answer first.

Correct answer: B

The correct answer is 2, 3, and 6..

  1. Identify the triangle information: List the angle measures, side lengths, center, segment, or proof relationship given in the problem.
  2. Apply the triangle theorem: The two smaller sides sum to 5, which is not greater than 6.
  3. Check the conclusion: The correct answer is 2, 3, and 6..

The two smaller sides sum to 5, which is not greater than 6.

3. QuestionMultiple choice

A triangle has sides 9, 13, and x. Which range allows a triangle?

Please select an answer first.

Correct answer: C

The correct answer is 4 < x < 22..

  1. Identify the triangle information: List the angle measures, side lengths, center, segment, or proof relationship given in the problem.
  2. Apply the triangle theorem: The Triangle Inequality Theorem gives |13 − 9| < x < 13 + 9, so 4 < x < 22.
  3. Check the conclusion: The correct answer is 4 < x < 22..

The Triangle Inequality Theorem gives |13 − 9| < x < 13 + 9, so 4 < x < 22.

4. QuestionMultiple choice

A triangle has angles 45° and 65°. What is its third angle?

Please select an answer first.

Correct answer: D

The correct answer is 70°..

  1. Identify the triangle information: List the angle measures, side lengths, center, segment, or proof relationship given in the problem.
  2. Apply the triangle theorem: The third angle is 180° − 45° − 65° = 70°.
  3. Check the conclusion: The correct answer is 70°..

The third angle is 180° − 45° − 65° = 70°.

5. QuestionMultiple choice

Two sides of a triangle measure 8 and 11. Which could be the third side?

Please select an answer first.

Correct answer: A

The correct answer is 4..

  1. Identify the triangle information: List the angle measures, side lengths, center, segment, or proof relationship given in the problem.
  2. Apply the triangle theorem: The third side must be greater than 3 and less than 19; 4 is possible.
  3. Check the conclusion: The correct answer is 4..

The third side must be greater than 3 and less than 19; 4 is possible.

6. QuestionMultiple choice

Which angle is opposite the longest side of a triangle?

Please select an answer first.

Correct answer: B

The correct answer is The largest angle..

  1. Identify the triangle information: List the angle measures, side lengths, center, segment, or proof relationship given in the problem.
  2. Apply the triangle theorem: The longest side is opposite the largest angle.
  3. Check the conclusion: The correct answer is The largest angle..

The longest side is opposite the largest angle.

7. QuestionMultiple choice

An isosceles triangle has two sides of length 7 and perimeter 24. What is the base length?

Please select an answer first.

Correct answer: C

The correct answer is 10..

  1. Identify the triangle information: List the angle measures, side lengths, center, segment, or proof relationship given in the problem.
  2. Apply the triangle theorem: Subtract the two equal sides from the perimeter: 24 − 7 − 7 = 10.
  3. Check the conclusion: The correct answer is 10..

Subtract the two equal sides from the perimeter: 24 − 7 − 7 = 10.

8. QuestionMultiple choice

What is the perimeter of a triangle with sides 6, 8, and 10?

Please select an answer first.

Correct answer: D

The correct answer is 24 units..

  1. Identify the triangle information: List the angle measures, side lengths, center, segment, or proof relationship given in the problem.
  2. Apply the triangle theorem: Add the side lengths: 6 + 8 + 10 = 24 units.
  3. Check the conclusion: The correct answer is 24 units..

Add the side lengths: 6 + 8 + 10 = 24 units.

9. QuestionMultiple choice

An exterior angle has remote interior angles 48° and 63°. What is its measure?

Please select an answer first.

Correct answer: A

The correct answer is 111°..

  1. Identify the triangle information: List the angle measures, side lengths, center, segment, or proof relationship given in the problem.
  2. Apply the triangle theorem: By the Exterior Angle Theorem, 48° + 63° = 111°.
  3. Check the conclusion: The correct answer is 111°..

By the Exterior Angle Theorem, 48° + 63° = 111°.

10. QuestionMultiple choice

An exterior angle measures 140° and one remote interior angle is 65°. What is the other?

Please select an answer first.

Correct answer: B

The correct answer is 75°..

  1. Identify the triangle information: List the angle measures, side lengths, center, segment, or proof relationship given in the problem.
  2. Apply the triangle theorem: The missing remote angle is 140° − 65° = 75°.
  3. Check the conclusion: The correct answer is 75°..

The missing remote angle is 140° − 65° = 75°.

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