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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

Two triangles share side AC. Which property proves AC is congruent to itself?

Please select an answer first.

Correct answer: A

The correct answer is The Reflexive Property..

  1. Identify the triangle information: List the side lengths, angle measures, vertices, or correspondence shown in the question.
  2. Apply the triangle rule: Every segment is congruent to itself by the Reflexive Property.
  3. Check the conclusion: The correct answer is The Reflexive Property..

Every segment is congruent to itself by the Reflexive Property.

2. QuestionMultiple choice

After proving two triangles congruent, what justifies a claim about a corresponding angle?

Please select an answer first.

Correct answer: B

The correct answer is CPCTC..

  1. Identify the triangle information: List the side lengths, angle measures, vertices, or correspondence shown in the question.
  2. Apply the triangle rule: CPCTC permits corresponding sides and angles to be declared congruent after the triangles are proven congruent.
  3. Check the conclusion: The correct answer is CPCTC..

CPCTC permits corresponding sides and angles to be declared congruent after the triangles are proven congruent.

3. QuestionMultiple choice

Two triangles have two congruent angles and the included side congruent. Which criterion applies?

Please select an answer first.

Correct answer: C

The correct answer is ASA..

  1. Identify the triangle information: List the side lengths, angle measures, vertices, or correspondence shown in the question.
  2. Apply the triangle rule: Two angles and their included side satisfy the ASA congruence criterion.
  3. Check the conclusion: The correct answer is ASA..

Two angles and their included side satisfy the ASA congruence criterion.

4. QuestionMultiple choice

Two triangles have three pairs of congruent corresponding sides. Which criterion applies?

Please select an answer first.

Correct answer: D

The correct answer is SSS..

  1. Identify the triangle information: List the side lengths, angle measures, vertices, or correspondence shown in the question.
  2. Apply the triangle rule: Three pairs of congruent corresponding sides satisfy SSS.
  3. Check the conclusion: The correct answer is SSS..

Three pairs of congruent corresponding sides satisfy SSS.

5. QuestionMultiple choice

Two triangles have two congruent sides and the included angle congruent. Which criterion applies?

Please select an answer first.

Correct answer: A

The correct answer is SAS..

  1. Identify the triangle information: List the side lengths, angle measures, vertices, or correspondence shown in the question.
  2. Apply the triangle rule: Two sides and the included angle satisfy the SAS congruence criterion.
  3. Check the conclusion: The correct answer is SAS..

Two sides and the included angle satisfy the SAS congruence criterion.

6. QuestionMultiple choice

Two triangles have two congruent angles and a non-included congruent side. Which criterion applies?

Please select an answer first.

Correct answer: B

The correct answer is AAS..

  1. Identify the triangle information: List the side lengths, angle measures, vertices, or correspondence shown in the question.
  2. Apply the triangle rule: Two angles and a non-included side satisfy AAS.
  3. Check the conclusion: The correct answer is AAS..

Two angles and a non-included side satisfy AAS.

7. QuestionMultiple choice

Two right triangles have congruent hypotenuses and one congruent leg. Which theorem applies?

Please select an answer first.

Correct answer: C

The correct answer is HL..

  1. Identify the triangle information: List the side lengths, angle measures, vertices, or correspondence shown in the question.
  2. Apply the triangle rule: The Hypotenuse-Leg theorem proves the two right triangles congruent.
  3. Check the conclusion: The correct answer is HL..

The Hypotenuse-Leg theorem proves the two right triangles congruent.

8. QuestionMultiple choice

Which additional fact would make an SSA diagram provable by SAS?

Please select an answer first.

Correct answer: D

The correct answer is The angle must be included between the two known sides..

  1. Identify the triangle information: List the side lengths, angle measures, vertices, or correspondence shown in the question.
  2. Apply the triangle rule: SAS requires the angle between the two known sides; a non-included SSA angle is insufficient.
  3. Check the conclusion: The correct answer is The angle must be included between the two known sides..

SAS requires the angle between the two known sides; a non-included SSA angle is insufficient.

9. QuestionMultiple choice

If △ABC ≅ △XYZ, which statement is true?

Please select an answer first.

Correct answer: A

The correct answer is AB ≅ XY..

  1. Identify the triangle information: List the side lengths, angle measures, vertices, or correspondence shown in the question.
  2. Apply the triangle rule: The correspondence order is A↔X, B↔Y, and C↔Z, so AB corresponds to XY.
  3. Check the conclusion: The correct answer is AB ≅ XY..

The correspondence order is A↔X, B↔Y, and C↔Z, so AB corresponds to XY.

10. QuestionMultiple choice

What is a valid structure for a triangle congruence proof?

Please select an answer first.

Correct answer: B

The correct answer is List givens, identify congruent parts, select a criterion, then use CPCTC if needed..

  1. Identify the triangle information: List the side lengths, angle measures, vertices, or correspondence shown in the question.
  2. Apply the triangle rule: A valid proof connects the givens to a congruence criterion before drawing conclusions about corresponding parts.
  3. Check the conclusion: The correct answer is List givens, identify congruent parts, select a criterion, then use CPCTC if needed..

A valid proof connects the givens to a congruence criterion before drawing conclusions about corresponding parts.

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