When one figure is a dilation of the other, we know that corresponding side lengths of the original figure and the dilated image are in the same proportion, and are all related by the same scale factor, . What is the relationship of corresponding angles in the original figure and the dilated image?

For example, if triangle is dilated, using center , with a scale factor of 2, we can verify experimentally that each angle in triangle is congruent to its corresponding angle in triangle .  is congruent to .  is congruent to .  is congruent to .

What is the image of a line not passing through the center of dilation? For example, what will be the image of line when it is dilated with center and a scale factor of 2? We can use congruent corresponding angles to show that line is taken to parallel line .

What is the image of a line passing through the center of dilation?

For example, what will be the image of line when it is dilated with center and a scale factor of ? When line is dilated with center and a scale factor of , line is unchanged, because dilations take points on a line through the center of a dilation to points on the same line, by definition.

So a dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.