Answer:
[tex]\triangle LKJ \sim \triangle LHG[/tex]
Step-by-step explanation:
Let suppose that JK and GH are parallel to each other and the length of JK is a multiple of the length of GH ([tex]JK = m\cdot GH[/tex]), then we know that [tex]\angle H \cong \angle J[/tex] and [tex]\angle G \cong \angle K[/tex] by alternate internal angles and [tex]\angle L_{1} \cong \angle L_{2}[/tex] by opposite angles, then [tex]KL = m\cdot GL[/tex] and [tex]HL = m\cdot JL[/tex]. Lastly, we conclude that [tex]\triangle LKJ \sim \triangle LHG[/tex]
