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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

What does it mean for two figures to be similar?

Please select an answer first.

Correct answer: A

The correct answer is They have the same shape and proportional corresponding sides..

  1. Identify the scale relationship: Compare a corresponding image length with its original length to find the scale factor.
  2. Apply the scale factor: Similar figures have equal corresponding angles and proportional corresponding side lengths.
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

Similar figures have equal corresponding angles and proportional corresponding side lengths.

2. QuestionMultiple choice

Are triangles with side lengths 3, 4, 5 and 6, 8, 10 similar?

Please select an answer first.

Correct answer: B

The correct answer is Yes, the scale factor is 2..

  1. Identify the scale relationship: Compare a corresponding image length with its original length to find the scale factor.
  2. Apply the scale factor: Each side in the second triangle is twice the corresponding side in the first.
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

Each side in the second triangle is twice the corresponding side in the first.

3. QuestionMultiple choice

A side of length 5 corresponds to an image side of length 15. What is the scale factor?

Please select an answer first.

Correct answer: C

The correct answer is 33.

  1. Identify the scale relationship: Compare a corresponding image length with its original length to find the scale factor.
  2. Apply the scale factor: The scale factor is 15div5=315\\div5=3.
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

The scale factor is 15div5=315\\div5=3.

4. QuestionMultiple choice

A side of length 7 corresponds to a side of length 21 in a similar figure. What is the scale factor?

Please select an answer first.

Correct answer: D

The correct answer is 33.

  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 corresponding image and original lengths: 21div7=321\\div7=3.
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

Divide corresponding image and original lengths: 21div7=321\\div7=3.

5. QuestionMultiple choice

A small figure has corresponding sides 4 and 6. A similar large figure has the side corresponding to 4 equal to 6. What is the side corresponding to 6?

Please select an answer first.

Correct answer: A

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: The scale factor is 6div4=frac326\\div4=\\frac{3}{2}, so 6(frac32)=96(\\frac{3}{2})=9.
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

The scale factor is 6div4=frac326\\div4=\\frac{3}{2}, so 6(frac32)=96(\\frac{3}{2})=9.

6. QuestionMultiple choice

A figure is enlarged by scale factor 2. A side originally 5 units becomes:

Please select an answer first.

Correct answer: B

The correct answer is 1010 units.

  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 by the scale factor: 2(5)=102(5)=10.
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

Multiply by the scale factor: 2(5)=102(5)=10.

7. QuestionMultiple choice

What happens to angle measures during a dilation?

Please select an answer first.

Correct answer: C

The correct answer is They stay the same..

  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 but change lengths unless the factor is 1.
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

Dilations preserve angle measures but change lengths unless the factor is 1.

8. QuestionMultiple choice

Are figures with side ratios frac23,frac46,frac57\\frac{2}{3},\\frac{4}{6},\\frac{5}{7} necessarily similar?

Please select an answer first.

Correct answer: D

The correct answer is No, because the ratios are not all equal..

  1. Identify the scale relationship: Compare a corresponding image length with its original length to find the scale factor.
  2. Apply the scale factor: The first two ratios equal frac23\\frac{2}{3}, but frac57\\frac{5}{7} is different.
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

The first two ratios equal frac23\\frac{2}{3}, but frac57\\frac{5}{7} is different.

9. QuestionMultiple choice

What happens when a figure is dilated by a scale factor frac13\\frac{1}{3}?

Please select an answer first.

Correct answer: A

The correct answer is It becomes one-third as long in every direction..

  1. Identify the scale relationship: Compare a corresponding image length with its original length to find the scale factor.
  2. Apply the scale factor: Every length is multiplied by frac13\\frac{1}{3}, while angle measures stay the same.
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

Every length is multiplied by frac13\\frac{1}{3}, while angle measures stay the same.

10. QuestionMultiple choice

Are rectangles measuring 4 by 6 and 8 by 12 similar?

Please select an answer first.

Correct answer: B

The correct answer is Yes, every corresponding length has scale factor 2..

  1. Identify the scale relationship: Compare a corresponding image length with its original length to find the scale factor.
  2. Apply the scale factor: Both dimensions of the second rectangle are twice the corresponding dimensions of the first.
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

Both dimensions of the second rectangle are twice the corresponding dimensions of the first.

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