## Elementary Geometry for College Students (6th Edition)

First, we need to prove $\triangle FED\cong\triangle GED$ by method SSS. 1. $\overline{DF}\cong\overline{DG}$ and $\overline{FE}\cong\overline{EG}$. (Given) 2. $\overline{DE}\cong\overline{DE}$ (Identity) Then we can deduce $\angle EDF\cong\angle EDG$. So, $\vec{DE}$ bisects $\angle FDG$
*PLANNING: First, we need to prove $\triangle FED\cong\triangle GED$. Then we can deduce $\angle EDF\cong\angle EDG$. So, $\vec{DE}$ bisects $\angle FDG$ 1. $\overline{DF}\cong\overline{DG}$ and $\overline{FE}\cong\overline{EG}$. (Given) 2. $\overline{DE}\cong\overline{DE}$ (Identity) So now we have all 3 sides of $\triangle FED$ are congruent with 3 corresponding sides of $\triangle GED$. Therefore, 3. $\triangle FED\cong\triangle GED$ (SSS) 4. $\angle EDF\cong\angle EDG$ (CPCTC) 5. $\vec{DE}$ bisects $\angle FDG$ (if an angle is divided into 2 congruent angles by a line, then that line bisects that angle)