Exploring Similar Polygons and Scale Factors

What is a necessary condition for polygons to be considered similar?

• They must have the same perimeter.

• They must be regular polygons.

• They must have congruent angles and proportional sides.

• They must have the same size.

What is the term used to describe the constant ratio between corresponding sides of similar polygons?

• Similarity ratio

• Proportionality constant

• Scale factor

• Congruence ratio

In the first example, if triangle ABC is similar to triangle DEF, and AB = 3 and DE = 7, what is the ratio of AB to DE?

• 7:3

• 1:2

• 3:7

• 2:1

In the first example, if AB = 3, DE = 7, and BC = x, DF = 9, what is the value of x?

• 3

• 6

• 9

• 27

In the second example, why is it important to separate the nested triangles before setting up proportions?

• To ensure the proportions are set up correctly

• To make the problem easier to visualize

• To avoid confusion with the lengths of sides

• All of the above

In the second example, if the small triangle has a side length of 4 and the large triangle has a corresponding side length of 6, what is the ratio of the small triangle to the large triangle?

• 1:1

• 3:2

• 2:3

• 4:6

In the final example, if a triangle has sides in the ratio 4:5:6 and a perimeter of 60, what is the length of the side corresponding to 4x?

• 20

• 16

• 12

• 24

In the final example, if the longest side of the similar triangle is 18, what is the length of the shortest side?

• 12

• 10

• 8

• 6

True or False: Any two regular hexagons are similar.

• True

• False

True or False: Any rectangle is similar to any square.

• False

• True