Dilations & Similar Figures

Front

What is a dilation in geometry?

Back

A dilation is a transformation that alters the size of a figure but maintains its shape. It is defined by a center point and a scale factor.

Front

What is a scale factor?

Back

The scale factor is a number that scales, or multiplies, the dimensions of a figure during a dilation. A scale factor greater than 1 enlarges the figure, while a scale factor between 0 and 1 reduces it.

Front

If a figure is dilated by a scale factor of 2, what happens to its dimensions?

Back

All dimensions of the figure are multiplied by 2, resulting in a figure that is twice as large in each direction.

Front

How do you determine if two figures are similar?

Back

Two figures are similar if their corresponding angles are equal and the lengths of their corresponding sides are proportional.

Front

What is the relationship between the lengths of corresponding sides in similar figures?

Back

The lengths of corresponding sides in similar figures are proportional to each other, and this ratio is known as the scale factor.

Front

If triangle ABC is similar to triangle DEF, and AB = 4, DE = 8, what is the scale factor?

Back

Front

What is the formula for finding the area of similar figures?

Back

Front

If the scale factor of a dilation is 3, and the area of the original figure is 10, what is the area of the dilated figure?

Back

Front

How do you set up a proportion to find a missing length in similar figures?

Back

Front

If two similar figures have a scale factor of 1/2, how does this affect their perimeters?

Back

The perimeter of the smaller figure will be half the perimeter of the larger figure, since the scale factor directly affects linear dimensions.