Question

question 13 of 45 which of the following statements is true? a. segment ed is congruent to segment dc b. the segment bd bisects segment c. the segment de bisects segment ac d. the segment is perpendicular to segment ec

Explanation:

Step1: Analyze congruence conditions

There is no information given to suggest that $\overline{ED}\cong\overline{DC}$. There are no equal - side or equal - angle relationships to support this.

Step2: Analyze bisection of $\overline{BC}$

There is no indication that $\overline{BD}$ bisects $\overline{BC}$. No equal - length segments of $\overline{BC}$ are shown.

Step3: Analyze bisection of $\overline{AC}$

We see that $AE = EC$ (the tick marks on $\overline{AE}$ and $\overline{EC}$ indicate they are of equal length). By the definition of a bisector (a line or segment that divides another segment into two equal parts), since $E$ is a point on $\overline{AC}$ such that $AE=EC$, $\overline{DE}$ bisects $\overline{AC}$.

Step4: Analyze perpendicularity to $\overline{EC}$

The right - angle symbol is at $\angle DEC$, but this just shows that $\overline{DE}\perp\overline{AC}$, not specifically $\overline{EC}$ in a way that is relevant to the main property being asked.

Answer:

C. the segment $\overline{DE}$ bisects segment $\overline{AC}$