Question

1. given $overline{ab}congoverline{fg}$, $overrightarrow{bf}$ bisects $overline{ac}$ and $overline{dg}$. prove $overline{bc}congoverline{df}$

Explanation:

Step1: Define bisect property

Since $\overrightarrow{BF}$ bisects $\overline{AC}$, we have $AB = BC$. Since $\overrightarrow{BF}$ bisects $\overline{DG}$, we have $DF=FG$.

Step2: Use given congruence

We are given that $\overline{AB}\cong\overline{FG}$. By the transitive - property of congruence, if $AB = BC$, $DF = FG$, and $AB=FG$, then $BC\cong DF$.

Answer:

The proof is completed as above, showing $\overline{BC}\cong\overline{DF}$.