Similar Figures & Dilations

Front

What are similar figures?

Back

Similar figures are shapes that have the same shape but may differ in size. Their corresponding angles are equal, and their corresponding sides are in proportion.

Front

What is a dilation in geometry?

Back

A dilation is a transformation that changes the size of a figure but not its shape. It involves a center point and a scale factor.

Front

What does the scale factor indicate in a dilation?

Back

The scale factor indicates how much larger or smaller the image will be compared to the original figure. A scale factor greater than 1 enlarges the figure, while a scale factor less than 1 reduces it.

Front

If triangle ABC is similar to triangle DEF, what can be said about their corresponding angles?

Back

The corresponding angles of similar triangles are equal.

Front

If two triangles are similar, how are their corresponding sides related?

Back

The lengths of the corresponding sides of similar triangles are proportional.

Front

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

Back

The algebraic rule for dilating a point (x, y) by a scale factor of k is (x, y) --> (kx, ky).

Front

If point C is at (2, 3) and is dilated by a scale factor of 3, what are the coordinates of C'?

Back

C' will be at (6, 9).

Front

True or False: The 'image' is the shape after the dilation.

Back

True.

Front

What is the relationship between the perimeters of similar figures?

Back

The ratios of the perimeters of similar figures are equal to the ratios of their corresponding sides.

Front

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

Back

The lengths of the sides of triangle DEF will be 6, 8, and 10.