Question

1. write the correct words, numbers or symbols to complete the sentences. (5 points)
2. point ___ is the midpoint of $overline{ac}$.
3. $overline{ce}cong$ ___
4. $angle eabcong$ ___
5. the relationship of $overline{ce}$ to $overline{ca}$ is that $ce =$ ___.
6. the relationship of $overline{ba}$ to $overline{bf}$ is that $ba =$ ___

Explanation:

Step1: Recall mid - point definition

A mid - point divides a line segment into two equal parts. Since there is no other information about the mid - point of $\overline{AC}$ and no mid - point marked in a standard way in the figure, we assume there is an error in the problem or lack of information for this part.

Step2: Identify congruent segments

From the figure, if we assume the markings of equal segments are correct, and there are two short lines on $\overline{CE}$ and $\overline{EA}$, so $\overline{CE}\cong\overline{EA}$.

Step3: Identify congruent angles

If we assume the markings of equal angles are correct, and there are two short arcs on $\angle EAB$ and $\angle FBA$, so $\angle EAB\cong\angle FBA$.

Step4: Determine segment ratio

Since $\overline{CE}\cong\overline{EA}$, then $CE=\frac{1}{2}CA$.

Step5: Determine segment ratio

If we assume the markings of equal segments on $\overline{AB}$ are correct and $AF = FB$, then $BA = 2BF$.

Answer:

1. (No clear answer from the given figure)
2. $\overline{EA}$
3. $\angle FBA$
4. $\frac{1}{2}CA$
5. $2BF$