Question

based only on the given information, it is guaranteed that $overline{ab}perpoverline{cd}$. given: $\triangle abc$, $overline{ac}congoverline{bc}$. a. true b. false

Explanation:

Step1: Recall isosceles - triangle property

In an isosceles triangle $\triangle ABC$ with $AC\cong BC$, the line segment from the vertex $C$ (the vertex opposite the base) to the mid - point of the base $AB$ is the perpendicular bisector of the base. But we have no information about point $D$ being the mid - point of $AB$.

Step2: Analyze the perpendicularity condition

Just because $AC = BC$ in $\triangle ABC$, we cannot be sure that the line $CD$ is perpendicular to $AB$. There is no given information about $D$ being the mid - point of $AB$ or any other information that would imply $\overline{AB}\perp\overline{CD}$.

Answer:

B. False