Dilations & Similar Figures

Front

What is a dilation in geometry?

Back

A dilation is a transformation that produces an image that is the same shape as the original, but is a different size. It is defined by a center point and a scale factor.

Front

What is a scale factor?

Back

The scale factor is a number that scales, or multiplies, the dimensions of a figure. A scale factor greater than 1 enlarges the figure, while a scale factor between 0 and 1 reduces it.

Front

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

Back

All dimensions of the figure are multiplied by 2, resulting in a figure that is twice as large in each direction.

Front

How do you determine if two figures are similar?

Back

Two figures are similar if their corresponding angles are equal and the lengths of their corresponding sides are proportional.

Front

What is the relationship between the lengths of corresponding sides in similar figures?

Back

The lengths of corresponding sides in similar figures are proportional to each other, and this ratio is the scale factor.

Front

If triangle ABC is similar to triangle A'B'C', and AB = 4, A'B' = 12, what is the scale factor?

Back

Front

What is the formula to find the scale factor when given two corresponding sides?

Back

Front

If a shape is dilated by a scale factor of 1/2, what happens to its size?

Back

The shape is reduced to half its original size in all dimensions.

Front

What does it mean for a scale factor to be negative?

Back

A negative scale factor indicates a reflection across the center point in addition to resizing the figure.

Front

If a rectangle has a length of 10 and is dilated by a scale factor of 3, what is the new length?

Back