Geometry Similarity & Proportionality 4

Question 1

The geometric mean of 4 and 9 is:

Accepted Answer

6

Answer

The geometric mean is √(4 × 9) = √36 = 6.

Question 2

If two triangles are similar by AA, which additional information is required to prove congruence?

Accepted Answer

One pair of corresponding sides equal

Answer

Similar triangles become congruent only when a pair of corresponding sides is equal.

Question 3

In a right triangle, the altitude to the hypotenuse is the geometric mean of the two:

Accepted Answer

Hypotenuse segments

Answer

The altitude equals the geometric mean of the two segments it creates on the hypotenuse.

Question 4

Two similar cones have radii 3 and 5. What is the ratio of their surface areas?

Accepted Answer

9:25

Answer

Surface area ratio is the square of the linear ratio: 3²:5² = 9:25.

Question 5

A proportion states a/b = c/d. Cross-multiplying gives:

Accepted Answer

ad = bc

Answer

Cross-multiplication of a/b = c/d yields ad = bc.

Geometry Practice Test