Dilations and Parts of 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 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

If a point (x, y) is dilated by a scale factor of k, what is the new point?

Back

The new point after dilation is (kx, ky).

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. This means their corresponding angles are equal and their corresponding sides are proportional.

Front

What is the AA similarity condition?

Back

The AA (Angle-Angle) similarity condition states that if two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.

Front

What is the SSS similarity condition?

Back

The SSS (Side-Side-Side) similarity condition states that if the corresponding sides of two triangles are in proportion, then the triangles are similar.

Front

What is the SAS similarity condition?

Back

The SAS (Side-Angle-Side) similarity condition states that if two sides of one triangle are in proportion to two sides of another triangle and the included angles are equal, then the triangles are similar.

Front

How do you find the scale factor between two similar figures?

Back

To find the scale factor, divide the length of a side of the image by the length of the corresponding side of the original figure.

Front

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

Back

The scale factor is 2, since 8/4 = 2.

Front

In a dilation, if the original figure has a perimeter of P and the scale factor is k, what is the perimeter of the dilated figure?

Back

The perimeter of the dilated figure is kP.