Question

6) Here is the image of triangle ABC and its dilation using center D and scale factor 2. Explain how you

know that segment A'B' is parallel to its corresponding side, segment AB.
DC CB
A'
B = C'
В'
Answer: I know that segment A'B' is parallel to segment AB because

Answer 1

Segment A'B' is parallel to segment AB because in a dilation, corresponding sides and angles are preserved. The dilation has a scale factor of 2 and uses center D, maintaining the direction and ensuring that A'B' and AB are parallel.

Step-by-step explanation:

I know that segment A'B' is parallel to segment AB because in a dilation, corresponding sides of the original figure and its image are always parallel. In addition, corresponding angles are congruent, therefore the angle between the corresponding sides remains the same.

Given that triangle ABC has been dilated from center D with a scale factor of 2 to create triangle A'B'C', all sides of the original triangle are extended away from the center of dilation in a way that preserves the angles of the triangle.

When a line is extended through a dilation, the angles with respect to other lines drawn through the same center of dilation are preserved, therefore the side A'B' is not only twice as long as AB, but it maintains the same direction, ensuring parallelism. Thus, as a result of these properties of dilation, side A'B' of triangle A'B'C' must be parallel to side AB of triangle ABC.