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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

What does a dilation with scale factor 4 do to a segment length?

Please select an answer first.

Correct answer: A

The correct answer is It multiplies the length by 4..

  1. Identify the proportional relationship: Match corresponding sides, angles, units, or scale factors before writing an equation.
  2. Apply the similarity rule: A dilation multiplies every distance from the center by the scale factor.
  3. Check the result: The correct answer is It multiplies the length by 4..

A dilation multiplies every distance from the center by the scale factor.

2. QuestionMultiple choice

What is the image of point (2, −1) after a dilation centered at the origin with scale factor 3?

Please select an answer first.

Correct answer: B

The correct answer is (6, −3)..

  1. Identify the proportional relationship: Match corresponding sides, angles, units, or scale factors before writing an equation.
  2. Apply the similarity rule: Multiply both coordinates by 3: (3·2, 3·(−1)) = (6, −3).
  3. Check the result: The correct answer is (6, −3)..

Multiply both coordinates by 3: (3·2, 3·(−1)) = (6, −3).

3. QuestionMultiple choice

If two similar triangles have corresponding sides 5 and 8, what is the ratio of the smaller to the larger side?

Please select an answer first.

Correct answer: C

The correct answer is 5:8..

  1. Identify the proportional relationship: Match corresponding sides, angles, units, or scale factors before writing an equation.
  2. Apply the similarity rule: The ratio of corresponding smaller to larger lengths is 5:8.
  3. Check the result: The correct answer is 5:8..

The ratio of corresponding smaller to larger lengths is 5:8.

4. QuestionMultiple choice

Why does a line parallel to one side of a triangle create similar triangles?

Please select an answer first.

Correct answer: D

The correct answer is It creates a pair of congruent corresponding angles, and the shared angle gives AA..

  1. Identify the proportional relationship: Match corresponding sides, angles, units, or scale factors before writing an equation.
  2. Apply the similarity rule: Parallel lines give a pair of congruent corresponding angles, and the shared vertex angle completes AA similarity.
  3. Check the result: The correct answer is It creates a pair of congruent corresponding angles, and the shared angle gives AA..

Parallel lines give a pair of congruent corresponding angles, and the shared vertex angle completes AA similarity.

5. QuestionMultiple choice

If corresponding sides of similar triangles are 7 and 21, what is the scale factor from smaller to larger?

Please select an answer first.

Correct answer: A

The correct answer is 3..

  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 21 ÷ 7 = 3.
  3. Check the result: The correct answer is 3..

The scale factor is 21 ÷ 7 = 3.

6. QuestionMultiple choice

If the length scale factor is 5, what is the area scale factor?

Please select an answer first.

Correct answer: B

The correct answer is 25..

  1. Identify the proportional relationship: Match corresponding sides, angles, units, or scale factors before writing an equation.
  2. Apply the similarity rule: Area scales by the square of the length factor: 52=255^2=25.
  3. Check the result: The correct answer is 25..

Area scales by the square of the length factor: 52=255^2=25.

7. QuestionMultiple choice

If similar triangles have side scale factor 3, what is the perimeter scale factor?

Please select an answer first.

Correct answer: C

The correct answer is 3..

  1. Identify the proportional relationship: Match corresponding sides, angles, units, or scale factors before writing an equation.
  2. Apply the similarity rule: Perimeters are sums of lengths, so they scale by 3.
  3. Check the result: The correct answer is 3..

Perimeters are sums of lengths, so they scale by 3.

8. QuestionMultiple choice

If similar solids have length scale factor 2, what is the volume scale factor?

Please select an answer first.

Correct answer: D

The correct answer is 8..

  1. Identify the proportional relationship: Match corresponding sides, angles, units, or scale factors before writing an equation.
  2. Apply the similarity rule: Volume scales by the cube of the length factor: 23=82^3=8.
  3. Check the result: The correct answer is 8..

Volume scales by the cube of the length factor: 23=82^3=8.

9. QuestionMultiple choice

Triangle P has coordinates (0,0), (4,0), and (0,3). A similar triangle has scale factor 2 from the origin. What is its hypotenuse?

Please select an answer first.

Correct answer: A

The correct answer is 10..

  1. Identify the proportional relationship: Match corresponding sides, angles, units, or scale factors before writing an equation.
  2. Apply the similarity rule: The original hypotenuse is 5 by the Pythagorean Theorem, and doubling gives 10.
  3. Check the result: The correct answer is 10..

The original hypotenuse is 5 by the Pythagorean Theorem, and doubling gives 10.

10. QuestionMultiple choice

A triangle has side lengths 6, 8, and 10. A similar triangle has scale factor 1.5. What is its side corresponding to 8?

Please select an answer first.

Correct answer: B

The correct answer is 12..

  1. Identify the proportional relationship: Match corresponding sides, angles, units, or scale factors before writing an equation.
  2. Apply the similarity rule: Multiply the corresponding length by 1.5: 8 · 1.5 = 12.
  3. Check the result: The correct answer is 12..

Multiply the corresponding length by 1.5: 8 · 1.5 = 12.

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