Question

given $overline{ed}congoverline{db}$, which statements about the figure are true? check all that apply. $square$ $overline{eb}$ is bisected by $overline{df}$. $square$ a is the mid - point of $overline{fc}$. $square$ $overline{fc}$ bisects $overline{db}$. $square$ $overline{eb}$ is a segment bisector. $square$ $fa=\frac{1}{2}fc$. $square$ $overline{da}congoverline{ab}$

Explanation:

Step1: Recall the definition of segment - bisector

A segment - bisector divides a segment into two equal parts. Given $\overline{ED}\cong\overline{DB}$, a point on the line that passes through the mid - point of $\overline{EB}$ can be a segment bisector.

Step2: Analyze each statement

• $\overline{EB}$ is bisected by $\overline{DF}$: Since $\overline{ED}\cong\overline{DB}$, $\overline{DF}$ (assuming $F$ is on the perpendicular bisector of $\overline{EB}$ or relevant line) can bisect $\overline{EB}$, this statement can be true.
• $A$ is the mid - point of $\overline{FC}$: There is no information in the given $\overline{ED}\cong\overline{DB}$ to suggest that $A$ is the mid - point of $\overline{FC}$, so this statement is false.
• $\overline{FC}$ bisects $\overline{DB}$: There is no information to support this. Just because $\overline{ED}\cong\overline{DB}$ does not mean $\overline{FC}$ bisects $\overline{DB}$, so this statement is false.
• $\overline{EB}$ is a segment bisector: Since $\overline{ED}\cong\overline{DB}$, $\overline{EB}$ is a segment that is bisected, not a segment bisector, so this statement is false.
• $FA=\frac{1}{2}FC$: There is no information in the given $\overline{ED}\cong\overline{DB}$ to suggest this relationship, so this statement is false.
• $\overline{DA}\cong\overline{AB}$: There is no information to support this. Just because $\overline{ED}\cong\overline{DB}$ does not mean $\overline{DA}\cong\overline{AB}$, so this statement is false.

Answer:

$\overline{EB}$ is bisected by $\overline{DF}$