Question

1. line segment cd is the perpendicular bisector of line segment ab. is line segment ab the perpendicular bisector of line segment cd?

Explanation:

Step1: Recall the definition of perpendicular bisector

A perpendicular bisector of a line - segment divides the line - segment into two equal parts and is perpendicular to it. Given that $CD$ is the perpendicular bisector of $AB$, we know that $AM = BM$ and $\angle AM C=\angle BM C = 90^{\circ}$. But we have no information about whether $A$ and $B$ are equidistant from $C$ and $D$ or if $AB$ is perpendicular to $CD$.

Step2: Analyze the general case

Just because $CD$ is the perpendicular bisector of $AB$, it does not necessarily mean that $AB$ is the perpendicular bisector of $CD$. For $AB$ to be the perpendicular bisector of $CD$, we would need $CM=DM$ and $\angle AM C = 90^{\circ}$ (which we already have from the first condition) and also that points $A$ and $B$ are equidistant from $C$ and $D$. There is no evidence from the given information that $CM = DM$.

Answer:

No