move options to the blanks to complete the proof that $\overline{bf}$ is the third median of triangle $abc$.
1. because $\overline{ae}$ and $\overline{cd}$ are medians, $\overline{bd} \cong \underline{\overline{da}}$ and $\overline{be} \cong \underline{\overline{bc}}$.
2. since $\overline{ak} \parallel \overline{dc}$, $\frac{bd}{da} = \frac{bj}{jk}$.
3. using substitution and the fact that $\overline{bd} \cong \overline{da}$, $1 = \frac{bj}{jk}$. this shows that $\overline{bj} \cong \overline{jk}$, which makes $j$ the m
4. because ____ connects the midpoints of $\overline{bc}$ and $\overline{bk}$, ____ $\parallel$ ____.
5. since it is also known that $\overline{dc} \parallel \overline{ak}$, $ajck$ is a parallelogram.
6. the diagonals of a parallelogram bisect each other, so ____ $\cong$ ____ and $\overline{bf}$ is the third median of the
options: $\overline{ae}$, $\overline{af}$, $\overline{bc}$, $\overline{bk}$, $\overline{da}$, $\overline{ec}$, $\overline{fc}$, $\overline{fk}$

Question

Accepted Answer

# Explanation:
## Step1: Fix median segment error
Median $\overline{AE}$ means $\overline{BE} \cong \overline{EC}$ (not $\overline{BC}$).
## Step2: Identify midpoint connector
$\overline{JE}$ connects midpoints of $\overline{BC}$ and $\overline{BK}$, so $\overline{JE} \parallel \overline{CK}$.
## Step3: Use substitution for ratio
Since $\overline{BD} \cong \overline{DA}$, $\frac{BD}{DA}=1$, so $1=\frac{BJ}{JK}$, meaning $\overline{BJ} \cong \overline{JK}$.
## Step4: Apply parallelogram diagonal rule
Diagonals of parallelogram $AJCK$ bisect each other, so $\overline{FC} \cong \overline{AF}$.

# Answer:
1. Corrected blank: $\boldsymbol{\overline{EC}}$ (for $\overline{BE} \cong \boldsymbol{\overline{EC}}$)
2. Blank 4: $\boldsymbol{\overline{JE}}$
3. Blank 5: $\boldsymbol{\overline{JE}} \parallel \boldsymbol{\overline{CK}}$
4. Blank 6: $\boldsymbol{\overline{AF}} \cong \boldsymbol{\overline{FC}}$

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QUESTION IMAGE

Question

Explanation:

Step1: Fix median segment error

Step2: Identify midpoint connector

Step3: Use substitution for ratio

Step4: Apply parallelogram diagonal rule

Answer: