Properties of Dilation and Similar Figures

Front

What is dilation in geometry?

Back

Dilation is a transformation that alters the size of a figure but keeps its shape the same. It is defined by a center point and a scale factor.

Front

What is a scale factor in dilation?

Back

The scale factor is a number that describes how much a figure is enlarged or reduced 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, making the figure twice as large.

Front

What does it mean for two figures to be similar?

Back

Two figures are similar if they have the same shape but not necessarily the same size. Their corresponding angles are equal, and their corresponding sides are in proportion.

Front

How do you find the missing side of a similar figure?

Back

To find the missing side, set up a proportion using the lengths of corresponding sides from the two similar figures.

Front

What is the relationship between the sides of similar figures?

Back

The ratios of the lengths of corresponding sides of similar figures are equal.

Front

If the scale factor of a dilation is 0.5, what type of dilation is it?

Back

It is a reduction dilation, as the scale factor is between 0 and 1.

Front

What is the formula for finding the area of a dilated figure?

Back

If the original area is A and the scale factor is k, the area of the dilated figure is A' = k^2 * A.

Front

What happens to the angles of a figure during dilation?

Back

The angles of a figure remain unchanged during dilation.

Front

If two triangles are similar, what can be said about their corresponding angles?

Back

The corresponding angles of similar triangles are equal.