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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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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

How are similar and congruent figures related?

Please select an answer first.

Correct answer: A

The correct answer is Congruent figures are similar with a scale factor of 1..

  1. Identify the proportional relationship: Match corresponding sides, angles, units, or scale factors before writing an equation.
  2. Apply the similarity rule: Congruent figures have equal corresponding lengths and angles, which is similarity with scale factor 1.
  3. Check the result: The correct answer is Congruent figures are similar with a scale factor of 1..

Congruent figures have equal corresponding lengths and angles, which is similarity with scale factor 1.

2. QuestionMultiple choice

A photograph is enlarged from 4 inches wide to 10 inches wide. What is the scale factor?

Please select an answer first.

Correct answer: B

The correct answer is 2.5..

  1. Identify the proportional relationship: Match corresponding sides, angles, units, or scale factors before writing an equation.
  2. Apply the similarity rule: Divide the new width by the original width: 10 ÷ 4 = 2.5.
  3. Check the result: The correct answer is 2.5..

Divide the new width by the original width: 10 ÷ 4 = 2.5.

3. QuestionMultiple choice

If two triangles are similar, what can be said about their corresponding angles?

Please select an answer first.

Correct answer: C

The correct answer is They are congruent..

  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, so corresponding angles are congruent.
  3. Check the result: The correct answer is They are congruent..

Similarity preserves angle measures, so corresponding angles are congruent.

4. QuestionMultiple choice

Which proof is enough to show two triangles are similar?

Please select an answer first.

Correct answer: D

The correct answer is Two pairs of corresponding angles are congruent..

  1. Identify the proportional relationship: Match corresponding sides, angles, units, or scale factors before writing an equation.
  2. Apply the similarity rule: Two congruent angle pairs establish AA similarity.
  3. Check the result: The correct answer is Two pairs of corresponding angles are congruent..

Two congruent angle pairs establish AA similarity.

5. QuestionMultiple choice

A 12-foot flagpole casts a 9-foot shadow. A nearby tree casts a 30-foot shadow at the same time. What is the tree height?

Please select an answer first.

Correct answer: A

The correct answer is 40 feet..

  1. Identify the proportional relationship: Match corresponding sides, angles, units, or scale factors before writing an equation.
  2. Apply the similarity rule: Set up a proportion: 12/9 = h/30, so h = 40 feet.
  3. Check the result: The correct answer is 40 feet..

Set up a proportion: 12/9 = h/30, so h = 40 feet.

6. QuestionMultiple choice

A 5-foot student casts a 3-foot shadow. A building casts a 24-foot shadow. What is the building height?

Please select an answer first.

Correct answer: B

The correct answer is 40 feet..

  1. Identify the proportional relationship: Match corresponding sides, angles, units, or scale factors before writing an equation.
  2. Apply the similarity rule: Use 5/3 = h/24, giving 3h = 120 and h = 40 feet.
  3. Check the result: The correct answer is 40 feet..

Use 5/3 = h/24, giving 3h = 120 and h = 40 feet.

7. QuestionMultiple choice

A scale drawing uses 2 cm for every 5 m. How many meters does 7.2 cm represent?

Please select an answer first.

Correct answer: C

The correct answer is 18 m..

  1. Identify the proportional relationship: Match corresponding sides, angles, units, or scale factors before writing an equation.
  2. Apply the similarity rule: The rate is 5/2 m per centimeter, so 7.2 · 5/2 = 18 m.
  3. Check the result: The correct answer is 18 m..

The rate is 5/2 m per centimeter, so 7.2 · 5/2 = 18 m.

8. QuestionMultiple choice

A blueprint scale is 1:100. A wall measures 4.6 cm on the blueprint. What is its actual length?

Please select an answer first.

Correct answer: D

The correct answer is 4.6 m..

  1. Identify the proportional relationship: Match corresponding sides, angles, units, or scale factors before writing an equation.
  2. Apply the similarity rule: 4.6 cm · 100 = 460 cm = 4.6 meters.
  3. Check the result: The correct answer is 4.6 m..

4.6 cm · 100 = 460 cm = 4.6 meters.

9. QuestionMultiple choice

If △ABC∼△DEF\triangle ABC\sim\triangle DEF and AB/DE = 2/5, what is the scale factor from ABC to DEF?

Please select an answer first.

Correct answer: A

The correct answer is 5/2..

  1. Identify the proportional relationship: Match corresponding sides, angles, units, or scale factors before writing an equation.
  2. Apply the similarity rule: The scale factor from ABC to DEF is larger divided by smaller: 5 ÷ 2 = 5/2.
  3. Check the result: The correct answer is 5/2..

The scale factor from ABC to DEF is larger divided by smaller: 5 ÷ 2 = 5/2.

10. QuestionMultiple choice

A similar triangle has a corresponding side of 18 when the original side is 12. What is the scale factor?

Please select an answer first.

Correct answer: B

The correct answer is 3/2..

  1. Identify the proportional relationship: Match corresponding sides, angles, units, or scale factors before writing an equation.
  2. Apply the similarity rule: The scale factor is 18/12 = 3/2.
  3. Check the result: The correct answer is 3/2..

The scale factor is 18/12 = 3/2.

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