Answer
False
Work Step by Step
m$\angle$D=180-50-60=70$^{\circ}$, so m$\angle$EDG is 35$^{\circ}$ and m$\angle$DGE=180-60-35=85$^{\circ}$. Since segment DE is across from the largest angle in the triangle it must be the largest side, therefore segment DG cannot be larger than it.
