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Similarity and Dilations Practice Tests

These Grade 8 Math practice tests cover similar figures, dilations, scale factors, coordinate rules, proportional sides, perimeters, areas, and real-world models.

Skills covered

  • Finding and applying scale factors
  • Using coordinate rules for dilations centered at the origin
  • Determining whether figures are similar or congruent
  • Scaling lengths, perimeters, and areas
  • Solving map, model, shadow, blueprint, and scale-drawing problems

How to use these practice tests

Match corresponding parts first. Use the image-to-original ratio as the scale factor, then apply \(k\) to lengths and \(k^2\) to areas.

For more Grade 8 Math practice, return to the Grade 8 Math category.

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Grade 8 Similarity and Dilations Practice Tests

Practice Grade 8 Math questions about similar figures, dilations, scale factors, coordinate rules, proportional sides, perimeters, areas, and applications.

Choose the best answer for each question. Compare corresponding lengths, use the scale factor, and remember that areas scale by the square of the factor.

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

A dilation has scale factor 2. Are the original and image figures congruent?

Please select an answer first.

Correct answer: A

The correct answer is No, they are similar but have different sizes..

  1. Identify the scale relationship: Compare a corresponding image length with its original length to find the scale factor.
  2. Apply the scale factor: A scale factor other than 1 changes lengths, so the figures are similar but not congruent.
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

A scale factor other than 1 changes lengths, so the figures are similar but not congruent.

2. QuestionMultiple choice

Which transformation always produces a congruent image?

Please select an answer first.

Correct answer: B

The correct answer is A translation.

  1. Identify the scale relationship: Compare a corresponding image length with its original length to find the scale factor.
  2. Apply the scale factor: Translations preserve all lengths and angles.
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

Translations preserve all lengths and angles.

3. QuestionMultiple choice

Two triangles have equal corresponding angles and proportional corresponding sides. What relationship do they have?

Please select an answer first.

Correct answer: C

The correct answer is They are similar..

  1. Identify the scale relationship: Compare a corresponding image length with its original length to find the scale factor.
  2. Apply the scale factor: Equal corresponding angles and proportional sides define similarity.
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

Equal corresponding angles and proportional sides define similarity.

4. QuestionMultiple choice

What is special about a dilation with scale factor 1?

Please select an answer first.

Correct answer: D

The correct answer is It produces a congruent figure with the same size..

  1. Identify the scale relationship: Compare a corresponding image length with its original length to find the scale factor.
  2. Apply the scale factor: Multiplying every length by 1 leaves the figure unchanged in size and shape.
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

Multiplying every length by 1 leaves the figure unchanged in size and shape.

5. QuestionMultiple choice

A side of length 12 becomes 18 under a dilation. What is the scale factor?

Please select an answer first.

Correct answer: A

The correct answer is 1.51.5.

  1. Identify the scale relationship: Compare a corresponding image length with its original length to find the scale factor.
  2. Apply the scale factor: Divide image by original: 18div12=1.518\\div12=1.5.
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

Divide image by original: 18div12=1.518\\div12=1.5.

6. QuestionMultiple choice

If all corresponding side lengths of two triangles are equal, what can be concluded?

Please select an answer first.

Correct answer: B

The correct answer is The triangles are congruent by SSS..

  1. Identify the scale relationship: Compare a corresponding image length with its original length to find the scale factor.
  2. Apply the scale factor: Three equal corresponding sides prove congruence by SSS.
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

Three equal corresponding sides prove congruence by SSS.

7. QuestionMultiple choice

What does a dilation preserve?

Please select an answer first.

Correct answer: C

The correct answer is Angle measures.

  1. Identify the scale relationship: Compare a corresponding image length with its original length to find the scale factor.
  2. Apply the scale factor: Dilations preserve angle measures and proportionality, but lengths, perimeter, and area can change.
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

Dilations preserve angle measures and proportionality, but lengths, perimeter, and area can change.

8. QuestionMultiple choice

If a dilation has scale factor 3, by what factor does area change?

Please select an answer first.

Correct answer: D

The correct answer is 99.

  1. Identify the scale relationship: Compare a corresponding image length with its original length to find the scale factor.
  2. Apply the scale factor: Area changes by k2=32=9k^2=3^2=9.
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

Area changes by k2=32=9k^2=3^2=9.

9. QuestionMultiple choice

If a figure has perimeter 10 and is dilated by scale factor 4, what is the image perimeter?

Please select an answer first.

Correct answer: A

The correct answer is 4040.

  1. Identify the scale relationship: Compare a corresponding image length with its original length to find the scale factor.
  2. Apply the scale factor: Perimeter is multiplied by 4: 4(10)=404(10)=40.
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

Perimeter is multiplied by 4: 4(10)=404(10)=40.

10. QuestionMultiple choice

A similar triangle has scale factor 2. A corresponding original side is 7. What is the image side?

Please select an answer first.

Correct answer: B

The correct answer is 1414.

  1. Identify the scale relationship: Compare a corresponding image length with its original length to find the scale factor.
  2. Apply the scale factor: Multiply the original side by the scale factor: 2(7)=142(7)=14.
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

Multiply the original side by the scale factor: 2(7)=142(7)=14.

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