Question

given \\( \overline { e d } \cong \overline { d b } \\), which statements about the figure are true? check all that apply \\( \square \overline { e b } \\) is bisected by \\( \overline { d f } \\) \\( \square \\) a is the midpoint of \\( \overline { f c } \\) \\( \square \overline { f c } \\) bisects \\( \overline { d b } \\) \\( \square \overline { e b } \\) is a segment bisector \\( \square f a = \frac { 1 } { 2 } f c \\) \\( \square \overline { d a } \cong \overline { a b } \\)

Explanation:

Step1: Analyze the first statement

Since $\overline{ED}\cong\overline{DB}$, it means that point $D$ divides $\overline{EB}$ into two equal parts. So, $\overline{EB}$ is bisected by $\overline{DF}$ (as $D$ lies on $\overline{DF}$).

Step2: Analyze the second statement

From the figure, we can assume that $A$ is the mid - point of $\overline{FC}$ (by the property of the figure construction related to the given congruent segments). So, $FA=\frac{1}{2}FC$.

Step3: Analyze the third statement

There is no information given in the problem (only $\overline{ED}\cong\overline{DB}$) to suggest that $A$ is the mid - point of $\overline{FC}$.

Step4: Analyze the fourth statement

$\overline{FC}$ does not bisect $\overline{DB}$. We know $\overline{ED}\cong\overline{DB}$, but there is no indication of a bisecting relationship with $\overline{FC}$.

Step5: Analyze the fifth statement

$\overline{EB}$ is not a segment bisector. A segment bisector is a line, ray, or segment that divides another segment into two equal parts. Here, $\overline{EB}$ is the segment being bisected.

Step6: Analyze the sixth statement

There is no information given to show that $\overline{DA}\cong\overline{AB}$.

Answer:

• $\overline{EB}$ is bisected by $\overline{DF}$
• $FA=\frac{1}{2}FC$