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 midpoint 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: Analyze each statement

• For $\overline{EB}$ is bisected by $\overline{DF}$: There is no indication of this in the given $\overline{CD}\cong\overline{DB}$.
• For $A$ is the midpoint of $\overline{FC}$: Given the markings on $\overline{FC}$ (equal segments), this is true.
• For $\overline{FC}$ bisects $\overline{DB}$: No evidence from $\overline{CD}\cong\overline{DB}$ to support this.
• For $\overline{EB}$ is a segment bisector: Since $A$ is the mid - point of $\overline{FC}$, and if we assume some congruence (from $\overline{CD}\cong\overline{DB}$ and possible triangle congruence), $\overline{EB}$ can be a segment bisector.
• For $FA=\frac{1}{2}FC$: As $A$ is the mid - point of $\overline{FC}$, this is true.
• For $\overline{DA}\cong\overline{AB}$: No information from $\overline{CD}\cong\overline{DB}$ to confirm this.

Answer:

A is the midpoint of $\overline{FC}$, $\overline{EB}$ is a segment bisector, $FA = \frac{1}{2}FC$