Question

activity 3: make a mark? give a reason here are intersecting lines ae and cd: 1. translate line ae by the directed line - segment from b to c. label the images of a, b, e as a, b, e. a. what is true about lines ae and ae? explain your reasoning.

Explanation:

Step1: Recall translation property

A translation is a rigid - motion transformation. Rigid - motion transformations preserve distance and angle measures.

Step2: Analyze line segments

When line segment $AE$ is translated to form $A'E'$ by the directed line segment from $B$ to $C$, the length of $AE$ and $A'E'$ are equal because translation is a rigid motion. Also, the orientation of the lines is the same, so $AE\parallel A'E'$.

Answer:

Lines $AE$ and $A'E'$ are parallel and congruent. This is because translation is a rigid - motion transformation that preserves distance (so $AE = A'E'$) and angle measures (so the lines are parallel).