Dilations, Scale Factors, & 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, using a scale factor.

Front

What is a scale factor?

Back

A scale factor is a number that scales, or multiplies, the dimensions of a figure during a dilation.

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 scale factor and the dimensions of similar figures?

Back

The dimensions of similar figures are proportional to the scale factor; if the scale factor is k, then each dimension of the original figure is multiplied by k.

Front

If the scale factor from ΔDEF to ΔABC is 1/2, what does this imply about the sizes of the triangles?

Back

It implies that ΔABC is half the size of ΔDEF.

Front

What is the scale factor if the dimensions of a figure are doubled?

Back

The scale factor is 2.

Front

If the scale factor is 4, how does this affect the area of the figure?

Back

The area of the figure increases by a factor of 4^2, or 16, because area scales with the square of the scale factor.

Front

What is the formula to find the scale factor between two similar figures?

Back

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

Front

If two triangles have a scale factor of 3, what is the ratio of their areas?

Back

The ratio of their areas is 3^2, or 9.

Front

What does it mean for two figures to be congruent?

Back

Two figures are congruent if they have the same shape and size, meaning all corresponding sides and angles are equal.