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Question

In the given figure, AB||CD and a transversal EF cuts them at G and H respectively.
If GL and HM are the bisectors of the alternate angles AGH and GHD respectively, prove that GL||HM.

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Solution

Given: ABCD, GL and HM are angle bisectors of AGH and GHD respectively.

Now,

AGH=GHD (alternate interior angles as ABCD)

12AGH=12GHD

LGH=GHM

But they also form a pair of equal interior angles.

Hence, GLHM [ if the angles of any pair of alternate interior angles are equal, then the lines are parallel]


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