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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 the Triangle Proportionality Theorem describe?

Please select an answer first.

Correct answer: A

The correct answer is A line parallel to one side of a triangle divides the other two sides proportionally..

  1. Identify the proportional relationship: Match corresponding sides, angles, units, or scale factors before writing an equation.
  2. Apply the similarity rule: A line parallel to one side of a triangle creates proportional segments on the other two sides.
  3. Check the result: The correct answer is A line parallel to one side of a triangle divides the other two sides proportionally..

A line parallel to one side of a triangle creates proportional segments on the other two sides.

2. QuestionMultiple choice

What does the converse of the Triangle Proportionality Theorem help prove?

Please select an answer first.

Correct answer: B

The correct answer is That a line is parallel to one side of a triangle..

  1. Identify the proportional relationship: Match corresponding sides, angles, units, or scale factors before writing an equation.
  2. Apply the similarity rule: If the two sides are divided proportionally, the converse can establish that the dividing segment is parallel to the third side.
  3. Check the result: The correct answer is That a line is parallel to one side of a triangle..

If the two sides are divided proportionally, the converse can establish that the dividing segment is parallel to the third side.

3. QuestionMultiple choice

What does the Angle Bisector Theorem compare?

Please select an answer first.

Correct answer: C

The correct answer is The two segments on the opposite side in the ratio of the adjacent sides..

  1. Identify the proportional relationship: Match corresponding sides, angles, units, or scale factors before writing an equation.
  2. Apply the similarity rule: An angle bisector divides the opposite side proportionally to the two adjacent side lengths.
  3. Check the result: The correct answer is The two segments on the opposite side in the ratio of the adjacent sides..

An angle bisector divides the opposite side proportionally to the two adjacent side lengths.

4. QuestionMultiple choice

A segment parallel to one side of a triangle cuts the other two sides. What happens to the smaller triangle?

Please select an answer first.

Correct answer: D

The correct answer is It is similar to the original triangle by AA..

  1. Identify the proportional relationship: Match corresponding sides, angles, units, or scale factors before writing an equation.
  2. Apply the similarity rule: The parallel segment creates corresponding congruent angles, so AA similarity applies.
  3. Check the result: The correct answer is It is similar to the original triangle by AA..

The parallel segment creates corresponding congruent angles, so AA similarity applies.

5. QuestionMultiple choice

A parallel segment divides two sides into lengths 6 and 9 on one side, and 8 and x on the other. What is x?

Please select an answer first.

Correct answer: A

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: Set the ratios equal: 6/9 = 8/x, so 6x = 72 and x = 12.
  3. Check the result: The correct answer is 12..

Set the ratios equal: 6/9 = 8/x, so 6x = 72 and x = 12.

6. QuestionMultiple choice

Three parallel lines cut two transversals. What relationship do the intercepted segments have?

Please select an answer first.

Correct answer: B

The correct answer is Corresponding intercepted segments are proportional..

  1. Identify the proportional relationship: Match corresponding sides, angles, units, or scale factors before writing an equation.
  2. Apply the similarity rule: The Intercept Theorem states that parallel lines divide transversals proportionally.
  3. Check the result: The correct answer is Corresponding intercepted segments are proportional..

The Intercept Theorem states that parallel lines divide transversals proportionally.

7. QuestionMultiple choice

What is a midsegment of a triangle?

Please select an answer first.

Correct answer: C

The correct answer is A segment joining the midpoints of two sides..

  1. Identify the proportional relationship: Match corresponding sides, angles, units, or scale factors before writing an equation.
  2. Apply the similarity rule: A triangle midsegment connects two side midpoints and is parallel to the third side with half its length.
  3. Check the result: The correct answer is A segment joining the midpoints of two sides..

A triangle midsegment connects two side midpoints and is parallel to the third side with half its length.

8. QuestionMultiple choice

If three parallel lines cut one transversal into 4 and 6 units, and another into 10 and x units, what is x?

Please select an answer first.

Correct answer: D

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: Corresponding segments are proportional: 4/6 = 10/x, so 4x = 60 and x = 15.
  3. Check the result: The correct answer is 15..

Corresponding segments are proportional: 4/6 = 10/x, so 4x = 60 and x = 15.

9. QuestionMultiple choice

Why can a person use a shadow to estimate a tree height?

Please select an answer first.

Correct answer: A

The correct answer is The tree and its shadow form a triangle similar to a person and the person’s shadow..

  1. Identify the proportional relationship: Match corresponding sides, angles, units, or scale factors before writing an equation.
  2. Apply the similarity rule: With the same sun angle, the height-to-shadow ratios are equal by AA similarity.
  3. Check the result: The correct answer is The tree and its shadow form a triangle similar to a person and the person’s shadow..

With the same sun angle, the height-to-shadow ratios are equal by AA similarity.

10. QuestionMultiple choice

A map scale is 1 inch = 12 miles. How far apart are two towns 3.5 inches apart on the map?

Please select an answer first.

Correct answer: B

The correct answer is 42 miles..

  1. Identify the proportional relationship: Match corresponding sides, angles, units, or scale factors before writing an equation.
  2. Apply the similarity rule: Multiply 3.5 by 12: 3.5 · 12 = 42 miles.
  3. Check the result: The correct answer is 42 miles..

Multiply 3.5 by 12: 3.5 · 12 = 42 miles.

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