Question

9. 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 ZAGH and
ZGHD respectively. prove that GL | HM.​

Answer 1

Answer:

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EXPLANATION;

"In the figure, AB is parallel to CD,

Hence, angle AGH = angle GHD (alternate interior angle)

12 angle AGH = 1/2 angle GHD

Since, GL and G M are bisectors of AGH and GHD

1/2 angle AGH = 1/2 angle GHD

Angle LGH angle GHM

If alternate interior angles are equal then the lines are parallel to each other.

Hence, LG is parallel to HM

Answer 2

Answer:

AB || CD

∴ ∠AGH = ∠GHD ( alternate interior angles )      -     (i)

∵GL and HM are bisectors of the above alt. int. angles,

∠AGL = ∠LGH = ∠GHM = ∠MHD     -     (ii)

∴1/2 ∠AGH = 1/2 ∠GHD  ( from i and ii )

∴ GL || HM as the alt. int. angles ∠LGH = ∠GHM