Question

here are intersecting lines ae and cd: 2. rotate line ae by 180 degrees around point c. label the images of a, b, e as a, b, e. a. what is true about lines ab and ab? explain your reasoning.

Explanation:

Step1: Recall rotation property

A 180 - degree rotation around a point is a half - turn. When a line is rotated 180 degrees around a point, the pre - image and the image are collinear.

Step2: Analyze lines AB and A'B'

Since line AE is rotated 180 degrees around point C to get A'E', and points A and B lie on line AE, their images A' and B' lie on the rotated line A'E'. Lines AB and A'B' are collinear. This is because a 180 - degree rotation around a point maps a line to a line that lies on the same straight - line path as the original line.

Answer:

Lines AB and A'B' are collinear.