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Similarity and Proportions Practice Tests

These Grade 10 Geometry practice tests develop proportional reasoning with ratios, scale factors, similar triangles, parallel-line theorems, dilations, coordinate geometry, and indirect measurement.

Skills covered

  • Writing and solving equivalent ratios, proportions, unit rates, and scale drawings
  • Applying AA, SAS, and SSS similarity criteria and matching corresponding parts
  • Using the Triangle Proportionality, Intercept, Midsegment, and Angle Bisector Theorems
  • Understanding how length, perimeter, area, and volume change under scale factors
  • Using dilations, coordinates, shadows, maps, blueprints, and other real-world similarity applications

How to use these practice tests

Label the correspondence first, then write ratios in the same order. Keep units consistent and distinguish the length scale factor from the area or volume scale factor.

For more Grade 10 Math practice, return to the Grade 10 Math category.

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5 Tests
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1. Test

Grade 10 Similarity and Proportions Practice Tests

Practice Grade 10 Geometry questions about ratios, proportions, scale factors, similar triangles, parallel lines, dilations, and real-world measurement.

Choose the best answer. Match corresponding parts, write a proportion, identify the similarity criterion, and check units and scale factors before solving.

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

What is a proportion?

Please select an answer first.

Correct answer: A

The correct answer is An equation stating that two ratios are equal..

  1. Identify the proportional relationship: Match corresponding sides, angles, units, or scale factors before writing an equation.
  2. Apply the similarity rule: A proportion sets two equivalent ratios equal, such as 34=1520\frac{3}{4}=\frac{15}{20}.
  3. Check the result: The correct answer is An equation stating that two ratios are equal..

A proportion sets two equivalent ratios equal, such as 34=1520\frac{3}{4}=\frac{15}{20}.

2. QuestionMultiple choice

If 34=x20\frac{3}{4}=\frac{x}{20}, what is x?

Please select an answer first.

Correct answer: B

The correct answer is 15..

  1. Identify the proportional relationship: Match corresponding sides, angles, units, or scale factors before writing an equation.
  2. Apply the similarity rule: Cross-multiply: 4x = 3 · 20, so x = 15.
  3. Check the result: The correct answer is 15..

Cross-multiply: 4x = 3 · 20, so x = 15.

3. QuestionMultiple choice

Which operation solves 58=x24\frac{5}{8}=\frac{x}{24}?

Please select an answer first.

Correct answer: C

The correct answer is Multiply 5 by 24 and divide by 8..

  1. Identify the proportional relationship: Match corresponding sides, angles, units, or scale factors before writing an equation.
  2. Apply the similarity rule: Use equivalent ratios or cross multiplication: x = (5 · 24) ÷ 8 = 15.
  3. Check the result: The correct answer is Multiply 5 by 24 and divide by 8..

Use equivalent ratios or cross multiplication: x = (5 · 24) ÷ 8 = 15.

4. QuestionMultiple choice

What is the scale factor from a smaller figure to a larger similar figure?

Please select an answer first.

Correct answer: D

The correct answer is The ratio of a larger corresponding length to the smaller corresponding length..

  1. Identify the proportional relationship: Match corresponding sides, angles, units, or scale factors before writing an equation.
  2. Apply the similarity rule: A scale factor compares corresponding lengths in the image and preimage.
  3. Check the result: The correct answer is The ratio of a larger corresponding length to the smaller corresponding length..

A scale factor compares corresponding lengths in the image and preimage.

5. QuestionMultiple choice

Which ratio is equivalent to 5:8?

Please select an answer first.

Correct answer: A

The correct answer is 15:24..

  1. Identify the proportional relationship: Match corresponding sides, angles, units, or scale factors before writing an equation.
  2. Apply the similarity rule: Multiply both parts of 5:8 by 3 to get 15:24.
  3. Check the result: The correct answer is 15:24..

Multiply both parts of 5:8 by 3 to get 15:24.

6. QuestionMultiple choice

A model uses 1 inch for every 4 feet. How many feet are represented by 7 inches?

Please select an answer first.

Correct answer: B

The correct answer is 28 feet..

  1. Identify the proportional relationship: Match corresponding sides, angles, units, or scale factors before writing an equation.
  2. Apply the similarity rule: Multiply the scale rate: 7 · 4 = 28 feet.
  3. Check the result: The correct answer is 28 feet..

Multiply the scale rate: 7 · 4 = 28 feet.

7. QuestionMultiple choice

If 7x=1418\frac{7}{x}=\frac{14}{18}, what is x?

Please select an answer first.

Correct answer: C

The correct answer is 9..

  1. Identify the proportional relationship: Match corresponding sides, angles, units, or scale factors before writing an equation.
  2. Apply the similarity rule: Cross-multiply: 7 · 18 = 14x, so 126 = 14x and x = 9.
  3. Check the result: The correct answer is 9..

Cross-multiply: 7 · 18 = 14x, so 126 = 14x and x = 9.

8. QuestionMultiple choice

A drawing uses a scale of 1:50. What does 6 cm represent?

Please select an answer first.

Correct answer: D

The correct answer is 300 cm..

  1. Identify the proportional relationship: Match corresponding sides, angles, units, or scale factors before writing an equation.
  2. Apply the similarity rule: Multiply the drawing length by 50: 6 · 50 = 300 centimeters.
  3. Check the result: The correct answer is 300 cm..

Multiply the drawing length by 50: 6 · 50 = 300 centimeters.

9. QuestionMultiple choice

Which pair of ratios forms a true proportion?

Please select an answer first.

Correct answer: A

The correct answer is 4:6 and 10:15..

  1. Identify the proportional relationship: Match corresponding sides, angles, units, or scale factors before writing an equation.
  2. Apply the similarity rule: Both 4:6 and 10:15 simplify to 2:3.
  3. Check the result: The correct answer is 4:6 and 10:15..

Both 4:6 and 10:15 simplify to 2:3.

10. QuestionMultiple choice

What is true about similar figures?

Please select an answer first.

Correct answer: B

The correct answer is Corresponding angles are congruent and corresponding side lengths are proportional..

  1. Identify the proportional relationship: Match corresponding sides, angles, units, or scale factors before writing an equation.
  2. Apply the similarity rule: Similarity preserves angle measures and proportional side relationships, but the figures can have different sizes.
  3. Check the result: The correct answer is Corresponding angles are congruent and corresponding side lengths are proportional..

Similarity preserves angle measures and proportional side relationships, but the figures can have different sizes.

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