Question

complete the following proof. reasons to be chosen from the bank provided on the last page.
given: $overline{cd}congoverline{ef}$, $overline{cd}congoverline{fg}$
prove: f is the mid - point of $overline{eg}$
statements\treasons

1. $overline{cd}congoverline{ef}$\t1. given
2. $overline{cd}congoverline{fg}$\t2. given

3.\t3. transitive property
4.\t4.

Explanation:

Step1: Identify given statements

We are given $\overline{CD}\cong\overline{EF}$ and $\overline{CD}\cong\overline{FG}$.

Step2: Apply transitive property

Since $\overline{CD}\cong\overline{EF}$ and $\overline{CD}\cong\overline{FG}$, by the transitive - property of congruence, we can say $\overline{EF}\cong\overline{FG}$.

Step3: Use mid - point definition

The definition of a mid - point states that if a point $F$ is the mid - point of a line segment $\overline{EG}$, then it divides $\overline{EG}$ into two congruent segments, which is consistent with $\overline{EF}\cong\overline{FG}$. The reason for the statement "F is the midpoint of $\overline{EG}$" is the definition of a mid - point.

Answer:

Definition of a mid - point