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Triangles and Congruence Practice Tests

These Grade 10 Geometry practice tests develop triangle vocabulary, classification, angle and side reasoning, congruence criteria, proof strategies, and coordinate applications.

Skills covered

  • Classifying triangles by sides and angles and applying the Triangle Sum, Exterior Angle, and Triangle Inequality Theorems
  • Using SSS, SAS, ASA, AAS, and HL to prove triangles congruent
  • Recognizing included sides and angles, corresponding parts, triangle notation, and CPCTC
  • Writing and checking congruence-proof reasoning with givens, properties, and theorems
  • Using coordinates, distance, midpoint, rigid motions, and the Pythagorean Theorem to analyze triangles

How to use these practice tests

Begin by marking the known sides, angles, and correspondence. Decide whether the information matches a valid congruence criterion before solving for a missing measure or applying CPCTC.

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

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Grade 10 Triangles and Congruence Practice Tests

Practice Grade 10 Geometry questions about triangle classification, angle and side relationships, congruence criteria, proofs, and coordinate geometry.

Choose the best answer. Classify the triangle or identify the correspondence, then apply the appropriate theorem, congruence criterion, formula, or proof step.

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

A triangle has angles 50° and 60°. What is the third angle?

Please select an answer first.

Correct answer: A

The correct answer is 70°..

  1. Identify the triangle information: List the side lengths, angle measures, vertices, or correspondence shown in the question.
  2. Apply the triangle rule: Use the Triangle Sum Theorem: 180° − 50° − 60° = 70°.
  3. Check the conclusion: The correct answer is 70°..

Use the Triangle Sum Theorem: 180° − 50° − 60° = 70°.

2. QuestionMultiple choice

An isosceles triangle has two base angles of 42°. What is its vertex angle?

Please select an answer first.

Correct answer: B

The correct answer is 96°..

  1. Identify the triangle information: List the side lengths, angle measures, vertices, or correspondence shown in the question.
  2. Apply the triangle rule: The two base angles total 84°, so the vertex angle is 180° − 84° = 96°.
  3. Check the conclusion: The correct answer is 96°..

The two base angles total 84°, so the vertex angle is 180° − 84° = 96°.

3. QuestionMultiple choice

An exterior angle is 120° and one remote interior angle is 45°. What is the other remote interior angle?

Please select an answer first.

Correct answer: C

The correct answer is 75°..

  1. Identify the triangle information: List the side lengths, angle measures, vertices, or correspondence shown in the question.
  2. Apply the triangle rule: By the Exterior Angle Theorem, the exterior angle equals the sum of the two remote interior angles: 120° = 45° + 75°.
  3. Check the conclusion: The correct answer is 75°..

By the Exterior Angle Theorem, the exterior angle equals the sum of the two remote interior angles: 120° = 45° + 75°.

4. QuestionMultiple choice

A right triangle has one acute angle of 35°. What is the other acute angle?

Please select an answer first.

Correct answer: D

The correct answer is 55°..

  1. Identify the triangle information: List the side lengths, angle measures, vertices, or correspondence shown in the question.
  2. Apply the triangle rule: The two acute angles of a right triangle are complementary, so 90° − 35° = 55°.
  3. Check the conclusion: The correct answer is 55°..

The two acute angles of a right triangle are complementary, so 90° − 35° = 55°.

5. QuestionMultiple choice

Which set of lengths can form a triangle?

Please select an answer first.

Correct answer: A

The correct answer is 4, 6, and 7..

  1. Identify the triangle information: List the side lengths, angle measures, vertices, or correspondence shown in the question.
  2. Apply the triangle rule: The sum of any two sides must exceed the third; 4 + 6 > 7, 4 + 7 > 6, and 6 + 7 > 4.
  3. Check the conclusion: The correct answer is 4, 6, and 7..

The sum of any two sides must exceed the third; 4 + 6 > 7, 4 + 7 > 6, and 6 + 7 > 4.

6. QuestionMultiple choice

If two sides of an isosceles triangle are congruent, what is true about the angles opposite them?

Please select an answer first.

Correct answer: B

The correct answer is They are congruent..

  1. Identify the triangle information: List the side lengths, angle measures, vertices, or correspondence shown in the question.
  2. Apply the triangle rule: The Isosceles Triangle Theorem states that angles opposite congruent sides are congruent.
  3. Check the conclusion: The correct answer is They are congruent..

The Isosceles Triangle Theorem states that angles opposite congruent sides are congruent.

7. QuestionMultiple choice

What is the measure of each angle in an equilateral triangle?

Please select an answer first.

Correct answer: C

The correct answer is 60°..

  1. Identify the triangle information: List the side lengths, angle measures, vertices, or correspondence shown in the question.
  2. Apply the triangle rule: All three angles are congruent and their sum is 180°, so each angle is 60°.
  3. Check the conclusion: The correct answer is 60°..

All three angles are congruent and their sum is 180°, so each angle is 60°.

8. QuestionMultiple choice

If an exterior angle measures 132° and one remote interior angle measures 58°, what is the other?

Please select an answer first.

Correct answer: D

The correct answer is 74°..

  1. Identify the triangle information: List the side lengths, angle measures, vertices, or correspondence shown in the question.
  2. Apply the triangle rule: The other remote interior angle is 132° − 58° = 74° by the Exterior Angle Theorem.
  3. Check the conclusion: The correct answer is 74°..

The other remote interior angle is 132° − 58° = 74° by the Exterior Angle Theorem.

9. QuestionMultiple choice

A triangle has side lengths 8, 10, and x. Which inequality describes possible values of x?

Please select an answer first.

Correct answer: A

The correct answer is 2 < x < 18..

  1. Identify the triangle information: List the side lengths, angle measures, vertices, or correspondence shown in the question.
  2. Apply the triangle rule: The Triangle Inequality Theorem gives |10 − 8| < x < 10 + 8, so 2 < x < 18.
  3. Check the conclusion: The correct answer is 2 < x < 18..

The Triangle Inequality Theorem gives |10 − 8| < x < 10 + 8, so 2 < x < 18.

10. QuestionMultiple choice

If an angle bisector in a triangle divides a 74° angle, what is the measure of each new angle?

Please select an answer first.

Correct answer: B

The correct answer is 37°..

  1. Identify the triangle information: List the side lengths, angle measures, vertices, or correspondence shown in the question.
  2. Apply the triangle rule: An angle bisector creates two congruent angles, so 74° ÷ 2 = 37°.
  3. Check the conclusion: The correct answer is 37°..

An angle bisector creates two congruent angles, so 74° ÷ 2 = 37°.

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