Similar Figures and Dilations

Front

What is a dilation in geometry?

Back

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

Front

What is the scale factor in a 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

How does dilation affect the perimeter of a figure?

Back

The perimeter of a figure is multiplied by the scale factor during a dilation.

Front

How does dilation affect the area of a figure?

Back

The area of a figure is multiplied by the square of the scale factor during a dilation.

Front

What is the difference between congruence and similarity?

Back

Congruence means two figures are the same shape and size, while similarity means two figures are the same shape but not necessarily the same size.

Front

What transformation preserves congruence?

Back

Transformations that preserve congruence include translations, rotations, and reflections.

Front

What transformation does NOT preserve congruence?

Back

Dilation does not preserve congruence because it changes the size of the figure.

Front

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

Back

The area is multiplied by 4 (2 squared) when a figure is dilated by a scale factor of 2.

Front

What is the formula for dilating a point (x,y) by a scale factor k?

Back

The formula is (x,y) -> (kx, ky).

Front

What is the relationship between corresponding sides of similar figures?

Back

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