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 definition of segment - bisector

A segment - bisector divides a segment into two equal parts. Given $\overline{ED}\cong\overline{DB}$, we check each statement.

Step2: Analyze $\overline{EB}$ is bisected by $\overline{DF}$

There is no information to suggest that $\overline{DF}$ divides $\overline{EB}$ into two equal parts, so this is false.

Step3: Analyze A is the mid - point of $\overline{FC}$

There is no information about the relationship between points A and the segment $\overline{FC}$ to suggest A is the mid - point, so this is false.

Step4: Analyze $\overline{FC}$ bisects $\overline{DB}$

There is no information to suggest that $\overline{FC}$ divides $\overline{DB}$ into two equal parts, so this is false.

Step5: Analyze $\overline{EB}$ is a segment bisector

Since $\overline{ED}\cong\overline{DB}$, $\overline{EB}$ is a segment bisector of $\overline{DB}$ (it contains the point D which divides $\overline{DB}$ into two equal segments), so this is true.

Step6: Analyze $FA=\frac{1}{2}FC$

There is no information about the relationship between FA and FC to suggest this, so this is false.

Step7: Analyze $\overline{DA}\cong\overline{AB}$

There is no information to suggest that $\overline{DA}$ and $\overline{AB}$ are congruent, so this is false.

Answer:

$\overline{EB}$ is a segment bisector.