Question

in given figure GM AND HL are bisector of angle AGH and angle GHD respectively such that GH II HL show that AB II CD

Answer 1

GM || HL are parallel so

angleMGH=GHL               (ALT. INT. ANGLES)

and ANGLE mgh =agm...(1)           (given angle bisector)

      ANGLE ghl=lhd...(2)                  (give)

Now,agm =lhd from 1 and 2}

Hence AGM AND LHD ARE ALT. INT. Anlgle for lines ab and cd and gh is transversal.

Hence AB || CD

Answer 2

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HERE'S THE ANSWER ✌
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GIVEN: GM is parallel to HL
so,

angle MGH=angle GHL
(alt. interior angles)
angle MGH= angle AGM.... i
(angle bisector)
angle GHL=angle LHD...... ii

now, AGM=LHD from i and ii

=>AGM and LHD are alternate interior angles for lines ab and cd

Hence,AB ll CD....... PROVED

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