OPM 2013 Problem 1

Consider a parallelogram $[ABCD]$ such that $\angle DAB$ is an acute angle. Let $G$ be a point in line $AB$ different from $B$ such that $\overline{BC}=\overline{GC}$ , and let $H$ be a point in line $BC$ different from $B$ such that $\overline{AB}=\overline{AH}$ . Prove that triangle $[GDH]$ is isosceles.