Prove congruence and use it to prove a further result

The following measurements describe two triangular shade panels

\(\triangle EFG\) and \(\triangle HGF\)

Lengths are in m

The lines EF and GH are parallel

The triangles use transversal FG

The two unshared vertices lie on opposite sides of the shared segment

The data give \(EF = HG = 9\,\mathrm{m}\)

Side \(FG\) is shared and has length \(9\,\mathrm{m}\)

The angle \(\angle EFG\) has measure \(120^\circ\)