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According to the question :-

It is already given that a transversal intersects two parallel lines 

We need to prove that bisctors of the alternate interior angles are parallel .......
                   → (i.e - GL is parallel to HM)


It is already given in the figure that EF is transversal , and AB and CD is parallel to one another .

⇒So , ∠ GHD = ∠ EGB ( Interior angle on the same side of the transversal )

Also ,
  \frac{1}{2}\ \textless \  GHD=  \frac{1}{2}\ \textless \  EGB

⇒ Hence we get ∠ MHD = ∠ LGB

→ Well , These are the angles which are formed by the line GL and Hm.....

→ Therefore  it is proved that GL and HM are parallel
                                      ∴ GL || HM

question is asked for alternate interior angles not for corresponding angels
I'd written the solution, which has been asked .............