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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

Which criterion proves two triangles similar when two angle pairs are congruent?

Please select an answer first.

Correct answer: A

The correct answer is AA..

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

AA similarity requires two pairs of congruent corresponding angles.

2. QuestionMultiple choice

What does SAS similarity require?

Please select an answer first.

Correct answer: B

The correct answer is Two proportional sides and the included angle congruent..

  1. Identify the proportional relationship: Match corresponding sides, angles, units, or scale factors before writing an equation.
  2. Apply the similarity rule: SAS similarity uses proportional corresponding sides with the included angle equal.
  3. Check the result: The correct answer is Two proportional sides and the included angle congruent..

SAS similarity uses proportional corresponding sides with the included angle equal.

3. QuestionMultiple choice

What does SSS similarity require?

Please select an answer first.

Correct answer: C

The correct answer is All three pairs of corresponding sides proportional..

  1. Identify the proportional relationship: Match corresponding sides, angles, units, or scale factors before writing an equation.
  2. Apply the similarity rule: SSS similarity is established when the three corresponding side ratios are equal.
  3. Check the result: The correct answer is All three pairs of corresponding sides proportional..

SSS similarity is established when the three corresponding side ratios are equal.

4. QuestionMultiple choice

If △ABC ~ △DEF, which vertex corresponds to C?

Please select an answer first.

Correct answer: D

The correct answer is F..

  1. Identify the proportional relationship: Match corresponding sides, angles, units, or scale factors before writing an equation.
  2. Apply the similarity rule: The order of the similarity statement gives A↔D, B↔E, and C↔F.
  3. Check the result: The correct answer is F..

The order of the similarity statement gives A↔D, B↔E, and C↔F.

5. QuestionMultiple choice

A similar figure has a scale factor of 3 from the original. What happens to each corresponding length?

Please select an answer first.

Correct answer: A

The correct answer is It is multiplied by 3..

  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 of 3 multiplies every corresponding length by 3.
  3. Check the result: The correct answer is It is multiplied by 3..

A scale factor of 3 multiplies every corresponding length by 3.

6. QuestionMultiple choice

Are triangles with side lengths 4, 6, 8 and 6, 9, 12 similar?

Please select an answer first.

Correct answer: B

The correct answer is Yes, because all corresponding side ratios equal 2:3..

  1. Identify the proportional relationship: Match corresponding sides, angles, units, or scale factors before writing an equation.
  2. Apply the similarity rule: The ratios 6/4, 9/6, and 12/8 are all 3/2, so SSS similarity applies.
  3. Check the result: The correct answer is Yes, because all corresponding side ratios equal 2:3..

The ratios 6/4, 9/6, and 12/8 are all 3/2, so SSS similarity applies.

7. QuestionMultiple choice

Which information is sufficient for AA similarity?

Please select an answer first.

Correct answer: C

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

  1. Identify the proportional relationship: Match corresponding sides, angles, units, or scale factors before writing an equation.
  2. Apply the similarity rule: Two angle pairs determine the third angle pair because triangle angle sums are 180 degrees.
  3. Check the result: The correct answer is Two pairs of congruent corresponding angles..

Two angle pairs determine the third angle pair because triangle angle sums are 180 degrees.

8. QuestionMultiple choice

In SAS similarity, which angle must be congruent?

Please select an answer first.

Correct answer: D

The correct answer is The angle included between the two proportional sides..

  1. Identify the proportional relationship: Match corresponding sides, angles, units, or scale factors before writing an equation.
  2. Apply the similarity rule: The SAS angle is the angle formed by the two sides whose lengths are proportional.
  3. Check the result: The correct answer is The angle included between the two proportional sides..

The SAS angle is the angle formed by the two sides whose lengths are proportional.

9. QuestionMultiple choice

If two triangles are similar with scale factor 2, how do their perimeters compare?

Please select an answer first.

Correct answer: A

The correct answer is The larger perimeter is twice the smaller perimeter..

  1. Identify the proportional relationship: Match corresponding sides, angles, units, or scale factors before writing an equation.
  2. Apply the similarity rule: Perimeter is a sum of lengths, so it scales by the same factor as the sides.
  3. Check the result: The correct answer is The larger perimeter is twice the smaller perimeter..

Perimeter is a sum of lengths, so it scales by the same factor as the sides.

10. QuestionMultiple choice

If two triangles are similar with scale factor 2, how do their areas compare?

Please select an answer first.

Correct answer: B

The correct answer is The larger area is four times the smaller area..

  1. Identify the proportional relationship: Match corresponding sides, angles, units, or scale factors before writing an equation.
  2. Apply the similarity rule: Areas scale by the square of the length factor: 22=42^2=4.
  3. Check the result: The correct answer is The larger area is four times the smaller area..

Areas scale by the square of the length factor: 22=42^2=4.

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