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:

A 180 - degree rotation around a point is a half - turn. When line $AE$ is rotated 180 degrees around point $C$, the resulting line $A'E'$ is collinear with the original line $AE$. Points $A$ and $B$ on line $AE$ are mapped to $A'$ and $B'$ respectively. Since a 180 - degree rotation around a point is an isometry that preserves collinearity and orientation in a sense that the new line segment $A'B'$ lies on the same straight line as $AB$. So, lines $AB$ and $A'B'$ are collinear.

Answer:

Lines $AB$ and $A'B'$ are collinear.