Question

Lulu observes that when she dilates a quadrilateral from a center of dilation outside the

quadrilateral, the corresponding sides of the original figure and its dilated image are
parallel. Which statement best explains why this occurs?

Answer 1

The corresponding sides of the original figure and its dilated image are parallel because dilation preserves shape while changing size.

Step-by-step explanation:

The reason why the corresponding sides of the original figure and its dilated image are parallel when dilating a quadrilateral from a center of dilation outside the quadrilateral is because dilation preserves the shape of the figure while changing the size.

When we dilate a figure, each side is stretched or shrunk by the same scale factor. This means that the angles between the sides remain the same, resulting in parallel corresponding sides in the original figure and its dilated image.

For example, if we have a quadrilateral ABCD and dilate it with a scale factor of 2, the corresponding sides AB and A'B' will be parallel, as well as BC and B'C', CD and C'D', and DA and D'A'.