Geometry Similarity & Proportionality 3

Question 1

Two similar solids have a scale factor of 2. What is the ratio of their volumes?

Accepted Answer

8:1

Answer

Volume ratio is the cube of the scale factor: 2³ = 8.

Question 2

In a triangle, the angle bisector divides the opposite side into segments proportional to the:

Accepted Answer

Adjacent sides

Answer

The Angle Bisector Theorem states the ratio equals the ratio of the two adjacent sides.

Question 3

If DE is parallel to BC in triangle ABC with AD = 4, DB = 6, and AE = 6, what is EC?

Accepted Answer

9

Answer

By proportionality 4/6 = 6/EC, so EC = 9.

Question 4

Two similar pentagons have areas 16 cm² and 81 cm². What is the ratio of their sides?

Accepted Answer

4:9

Answer

Take the square root of the area ratio: √16:√81 = 4:9.

Question 5

Which of the following always produces similar figures?

Accepted Answer

A dilation

Answer

A dilation preserves shape and angles, producing a similar figure.

Geometry Practice Test