NumicornNumicornLearn, solve, progress

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.

Select a test

5 Tests
1. Test2. Test3. Test4. Test5. Test

5. Test

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 formula gives the distance between two coordinate points?

Please select an answer first.

Correct answer: A

The correct answer is d=(x2−x1)2+(y2−y1)2d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}..

  1. Identify the triangle information: List the side lengths, angle measures, vertices, or correspondence shown in the question.
  2. Apply the triangle rule: The distance formula comes from the Pythagorean Theorem applied to horizontal and vertical changes.
  3. Check the conclusion: The correct answer is d=(x2−x1)2+(y2−y1)2d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}..

The distance formula comes from the Pythagorean Theorem applied to horizontal and vertical changes.

2. QuestionMultiple choice

What is the midpoint of points (−2,4)(-2,4) and 6,86,8?

Please select an answer first.

Correct answer: B

The correct answer is (2,6)(2,6)..

  1. Identify the triangle information: List the side lengths, angle measures, vertices, or correspondence shown in the question.
  2. Apply the triangle rule: Average the coordinates: ((−2 + 6)/2, (4 + 8)/2) = (2, 6).
  3. Check the conclusion: The correct answer is (2,6)(2,6)..

Average the coordinates: ((−2 + 6)/2, (4 + 8)/2) = (2, 6).

3. QuestionMultiple choice

Which transformation always preserves triangle congruence?

Please select an answer first.

Correct answer: C

The correct answer is A translation..

  1. Identify the triangle information: List the side lengths, angle measures, vertices, or correspondence shown in the question.
  2. Apply the triangle rule: A translation is a rigid motion that preserves distances and angle measures.
  3. Check the conclusion: The correct answer is A translation..

A translation is a rigid motion that preserves distances and angle measures.

4. QuestionMultiple choice

What does a reflection preserve?

Please select an answer first.

Correct answer: D

The correct answer is Distances and angle measures..

  1. Identify the triangle information: List the side lengths, angle measures, vertices, or correspondence shown in the question.
  2. Apply the triangle rule: Reflection is a rigid motion, so it preserves size and shape even though orientation is reversed.
  3. Check the conclusion: The correct answer is Distances and angle measures..

Reflection is a rigid motion, so it preserves size and shape even though orientation is reversed.

5. QuestionMultiple choice

The points (0, 0), (3, 0), and (0, 4) form a right triangle. What is the length of the hypotenuse?

Please select an answer first.

Correct answer: A

The correct answer is 5..

  1. Identify the triangle information: List the side lengths, angle measures, vertices, or correspondence shown in the question.
  2. Apply the triangle rule: The legs have lengths 3 and 4, so c=32+42=5c=\sqrt{3^2+4^2}=5.
  3. Check the conclusion: The correct answer is 5..

The legs have lengths 3 and 4, so c=32+42=5c=\sqrt{3^2+4^2}=5.

6. QuestionMultiple choice

If two triangles are congruent, what can be said about their areas?

Please select an answer first.

Correct answer: B

The correct answer is Their areas are equal..

  1. Identify the triangle information: List the side lengths, angle measures, vertices, or correspondence shown in the question.
  2. Apply the triangle rule: Congruent triangles have the same shape and size, so their corresponding areas are equal.
  3. Check the conclusion: The correct answer is Their areas are equal..

Congruent triangles have the same shape and size, so their corresponding areas are equal.

7. QuestionMultiple choice

If two triangles are congruent, what can be said about their perimeters?

Please select an answer first.

Correct answer: C

The correct answer is Their perimeters are equal..

  1. Identify the triangle information: List the side lengths, angle measures, vertices, or correspondence shown in the question.
  2. Apply the triangle rule: Congruent triangles have three pairs of equal corresponding side lengths, so their perimeter sums are equal.
  3. Check the conclusion: The correct answer is Their perimeters are equal..

Congruent triangles have three pairs of equal corresponding side lengths, so their perimeter sums are equal.

8. QuestionMultiple choice

Which transformation turns a figure around a fixed point without changing its size?

Please select an answer first.

Correct answer: D

The correct answer is A rotation..

  1. Identify the triangle information: List the side lengths, angle measures, vertices, or correspondence shown in the question.
  2. Apply the triangle rule: A rotation is a rigid motion that moves every point around a center while preserving distances and angles.
  3. Check the conclusion: The correct answer is A rotation..

A rotation is a rigid motion that moves every point around a center while preserving distances and angles.

9. QuestionMultiple choice

Two triangles have corresponding side lengths 5, 7, and 9. What can be concluded?

Please select an answer first.

Correct answer: A

The correct answer is They are congruent by 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 equal corresponding sides satisfy the SSS congruence criterion.
  3. Check the conclusion: The correct answer is They are congruent by SSS..

Three pairs of equal corresponding sides satisfy the SSS congruence criterion.

10. QuestionMultiple choice

Why are triangular braces common in structures?

Please select an answer first.

Correct answer: B

The correct answer is A triangle keeps its shape when its side lengths are fixed..

  1. Identify the triangle information: List the side lengths, angle measures, vertices, or correspondence shown in the question.
  2. Apply the triangle rule: Triangle rigidity means fixed side lengths determine the triangle up to congruence, making triangular bracing stable.
  3. Check the conclusion: The correct answer is A triangle keeps its shape when its side lengths are fixed..

Triangle rigidity means fixed side lengths determine the triangle up to congruence, making triangular bracing stable.

Previous testNext test