Geometry Similarity & Proportionality 2

Question 1

Two triangles are similar with a scale factor of 3. If the smaller triangle has a perimeter of 12 cm, what is the perimeter of the larger triangle?

Accepted Answer

36 cm

Answer

Perimeter scales by the same factor as the sides, so 12 × 3 = 36 cm.

Question 2

In similar figures, the ratio of areas equals the ratio of corresponding sides:

Accepted Answer

Squared

Answer

Area ratio is the square of the linear scale factor.

Question 3

A line parallel to one side of a triangle divides the other two sides proportionally. This is known as the:

Accepted Answer

Triangle Proportionality Theorem

Answer

The Triangle Proportionality (Basic Proportionality) Theorem states a parallel line cuts the sides proportionally.

Question 4

If two triangles have all three pairs of angles equal, they are guaranteed to be:

Accepted Answer

Similar

Answer

Equal corresponding angles (AA/AAA) guarantees similarity but not congruence.

Question 5

A 6 ft person casts a 4 ft shadow while a nearby tree casts a 20 ft shadow. How tall is the tree?

Accepted Answer

30 ft

Answer

Set up 6/4 = h/20, giving h = 30 ft.

Geometry Practice Test