# If a transversal intersects two parallel lines, then prove that bisectors of alternate interior angles are parallel

1
by arifalam

2015-09-26T10:03:40+05:30

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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)

PROOF :-

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 ,

⇒ 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 .............