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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

Which congruence criterion uses three pairs of congruent sides?

Please select an answer first.

Correct answer: A

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: Side-Side-Side congruence proves triangles congruent when all three corresponding side pairs are congruent.
  3. Check the conclusion: The correct answer is SSS..

Side-Side-Side congruence proves triangles congruent when all three corresponding side pairs are congruent.

2. QuestionMultiple choice

What does SAS stand for?

Please select an answer first.

Correct answer: B

The correct answer is Side-Angle-Side..

  1. Identify the triangle information: List the side lengths, angle measures, vertices, or correspondence shown in the question.
  2. Apply the triangle rule: SAS uses two congruent sides and the included angle between those sides.
  3. Check the conclusion: The correct answer is Side-Angle-Side..

SAS uses two congruent sides and the included angle between those sides.

3. QuestionMultiple choice

Which criterion uses two angles and the included side?

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: Angle-Side-Angle uses two congruent angles and the side between them.
  3. Check the conclusion: The correct answer is ASA..

Angle-Side-Angle uses two congruent angles and the side between them.

4. QuestionMultiple choice

What does AAS use to prove triangles congruent?

Please select an answer first.

Correct answer: D

The correct answer is Two angles and a non-included side..

  1. Identify the triangle information: List the side lengths, angle measures, vertices, or correspondence shown in the question.
  2. Apply the triangle rule: Angle-Angle-Side uses two congruent angles and a corresponding side that is not between the angles.
  3. Check the conclusion: The correct answer is Two angles and a non-included side..

Angle-Angle-Side uses two congruent angles and a corresponding side that is not between the angles.

5. QuestionMultiple choice

Which criterion proves two right triangles congruent using the hypotenuse and one leg?

Please select an answer first.

Correct answer: A

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 applies to right triangles when the hypotenuse and one corresponding leg are congruent.
  3. Check the conclusion: The correct answer is HL..

The Hypotenuse-Leg theorem applies to right triangles when the hypotenuse and one corresponding leg are congruent.

6. QuestionMultiple choice

Why is SSA generally not a triangle congruence theorem?

Please select an answer first.

Correct answer: B

The correct answer is The information can produce more than one possible triangle..

  1. Identify the triangle information: List the side lengths, angle measures, vertices, or correspondence shown in the question.
  2. Apply the triangle rule: Side-Side-Angle can create an ambiguous case, so it does not generally guarantee congruence.
  3. Check the conclusion: The correct answer is The information can produce more than one possible triangle..

Side-Side-Angle can create an ambiguous case, so it does not generally guarantee congruence.

7. QuestionMultiple choice

What does CPCTC mean?

Please select an answer first.

Correct answer: C

The correct answer is Corresponding Parts of Congruent Triangles 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: After proving triangles congruent, CPCTC allows any corresponding sides or angles to be identified as congruent.
  3. Check the conclusion: The correct answer is Corresponding Parts of Congruent Triangles are Congruent..

After proving triangles congruent, CPCTC allows any corresponding sides or angles to be identified as congruent.

8. QuestionMultiple choice

If triangle ABC corresponds to triangle DEF, which vertex corresponds to B?

Please select an answer first.

Correct answer: D

The correct answer is E..

  1. Identify the triangle information: List the side lengths, angle measures, vertices, or correspondence shown in the question.
  2. Apply the triangle rule: The order of the names gives the correspondence: A matches D, B matches E, and C matches F.
  3. Check the conclusion: The correct answer is E..

The order of the names gives the correspondence: A matches D, B matches E, and C matches F.

9. QuestionMultiple choice

In SAS, which angle must be known?

Please select an answer first.

Correct answer: A

The correct answer is The angle included between the two given sides..

  1. Identify the triangle information: List the side lengths, angle measures, vertices, or correspondence shown in the question.
  2. Apply the triangle rule: The SAS angle is the included angle formed by the two sides being compared.
  3. Check the conclusion: The correct answer is The angle included between the two given sides..

The SAS angle is the included angle formed by the two sides being compared.

10. QuestionMultiple choice

In ASA, which side is the included side?

Please select an answer first.

Correct answer: B

The correct answer is The side between the two given angles..

  1. Identify the triangle information: List the side lengths, angle measures, vertices, or correspondence shown in the question.
  2. Apply the triangle rule: The included side has the two specified angles at its endpoints.
  3. Check the conclusion: The correct answer is The side between the two given angles..

The included side has the two specified angles at its endpoints.

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