Similarity : Measuring Dilations

Front

What is the definition of similarity in geometry?

Back

Similarity in geometry refers to figures that have the same shape but may differ in size. Corresponding angles are equal, and corresponding sides are proportional.

Front

What is a dilation in geometry?

Back

A dilation is a transformation that alters the size of a figure but keeps its shape. It is defined by a center of dilation and a scale factor.

Front

What is the center of dilation?

Back

The center of dilation is a fixed point in the plane about which all points of a figure are expanded or contracted.

Front

How do you determine the scale factor in a dilation?

Back

The scale factor is determined by the ratio of the lengths of corresponding sides of the original figure and the dilated figure.

Front

If a triangle has sides of lengths 3, 4, and 5, and is dilated by a scale factor of 2, what are the lengths of the sides of the new triangle?

Back

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

Front

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

Back

The angles of a figure remain unchanged during a dilation.

Front

If the center of dilation is Point B, what does that imply about the transformation?

Back

It implies that all points of the figure will move away from or towards Point B based on the scale factor.

Front

What is the relationship between corresponding angles in similar figures?

Back

Corresponding angles in similar figures are equal.

Front

What is the relationship between corresponding sides in similar figures?

Back

Corresponding sides in similar figures are proportional.

Front

If a figure is dilated by a scale factor of 1, what happens to the figure?

Back

If a figure is dilated by a scale factor of 1, the figure remains unchanged.