Dilations and Similarity

Front

What is a dilation in geometry?

Back

A dilation is a transformation that alters the size of a figure but not its shape, using a center point and a scale factor.

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, meaning their corresponding angles are equal and their corresponding sides are in proportion.

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.

Front

If a triangle has sides of lengths 3, 4, and 5, what are the lengths of the sides of a similar triangle with a scale factor of 2?

Back

The lengths of the sides would be 6, 8, and 10.

Front

What is the similarity ratio?

Back

The similarity ratio is the ratio of the lengths of corresponding sides of two similar figures.

Front

If triangle ABC is similar to triangle DEF, and the length of side AB is 4 and side DE is 8, what is the similarity ratio?

Back

The similarity ratio is 1/2.

Front

What happens to the angles of a figure during a dilation?

Back

The angles remain unchanged during a dilation.

Front

How do you find the coordinates of a point after dilation?

Back

Multiply the coordinates of the original point by the scale factor.

Front

What is the coordinate of the image of point A (2, 3) under a dilation with center at the origin and scale factor k = 3?

Back

The coordinate of the image is (6, 9).

Front

Are the triangles with sides 5, 12, 13 and 10, 24, 26 similar?

Back

Yes, they are similar because their corresponding sides are in proportion.