Understanding Similar Polygons

The video tutorial explains the concept of similar polygons, focusing on the equality of corresponding angles and the ratios of side lengths, perimeters, and areas. It uses two rectangles as examples to demonstrate these concepts. The tutorial shows that the ratio of the perimeters of similar polygons is the same as the ratio of their corresponding side lengths. Additionally, it explains that the ratio of the areas is the square of the ratio of the side lengths.

What must be true for two polygons to be considered similar?

• Their corresponding sides must be equal.

• Their corresponding angles must be equal.

• Their areas must be equal.

• Their perimeters must be equal.

If one rectangle has sides of 5 and 2.5, and another has sides of 2.5 and 1, what is the ratio of their corresponding sides?

• 4:1

• 5:2

• 2:1

• 3:1

What is the perimeter of a rectangle with sides 5 and 2?

• 10 units

• 14 units

• 16 units

• 12 units

If the perimeter of one rectangle is 14 units and the perimeter of a similar rectangle is 7 units, what is the ratio of their perimeters?

• 3:1

• 4:1

• 5:2

• 2:1

What can be concluded if the ratio of the sides of two similar polygons is 2:1?

• The ratio of their perimeters is 2:1.

• The ratio of their areas is 1:1.

• The ratio of their areas is 2:1.

• The ratio of their perimeters is 4:1.

What is the area of a rectangle with sides 5 and 2?

• 14 square units

• 12 square units

• 10 square units

• 7 square units

If the area of one rectangle is 10 square units and the area of a similar rectangle is 2.5 square units, what is the ratio of their areas?

• 4:1

• 2:1

• 3:1

• 5:2

How is the ratio of the areas of two similar polygons related to the ratio of their sides?

• It is half the ratio of their sides.

• It is the same as the ratio of their sides.

• It is the cube of the ratio of their sides.

• It is the square of the ratio of their sides.

If the ratio of the sides of two similar polygons is 2:1, what is the ratio of their areas?

• 4:1

• 3:1

• 2:1

• 1:1

What is the area of a rectangle with sides 2.5 and 1?

• 2.75 square units

• 2 square units

• 3 square units

• 2.5 square units