Dilations and Similarity

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 scale factor that determines how much the figure is enlarged or reduced.

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 congruent, and their corresponding sides are proportional.

Front

What is the scale factor in dilations?

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 indicates enlargement, while a scale factor less than 1 indicates reduction.

Front

If triangle ABC is dilated by a scale factor of 2, what happens to its dimensions?

Back

The dimensions of triangle ABC will be doubled, making it larger while maintaining the same shape.

Front

What are corresponding angles in similar figures?

Back

Corresponding angles are angles in two or more figures that are in the same relative position. In similar figures, these angles are congruent.

Front

What are corresponding sides in similar figures?

Back

Corresponding sides are the sides in two or more figures that are in the same relative position. In similar figures, these sides are proportional.

Front

How do you find the area of a dilated figure?

Back

To find the area of a dilated figure, square the scale factor and multiply it by the area of the original figure.

Front

What is the relationship between the perimeters of similar figures?

Back

The ratio of the perimeters of similar figures is equal to the ratio of their corresponding sides.

Front

If a rectangle has dimensions 4 ft by 6 ft and is dilated by a scale factor of 3, what are the new dimensions?

Back

The new dimensions will be 12 ft by 18 ft.

Front

What is the formula for calculating the scale factor between two similar figures?

Back

The scale factor can be calculated by dividing the length of a side of one figure by the length of the corresponding side of the other figure.