Question

In the given figure, GM and HL are bisectors of AGH and GHD respectively, such that GM ║ HL. Show that AB ║ CD.

Answer 1

Since GM and HL are the bisectors of angle AGH and angle GHD,

angle AGM = angle MGH --- (1)
angle GHL = angle LHD --- (2)

but angle MGH = angle GHL [GM || HL] --- (3)
adding (1) and (2), we get,
angle AGM + angle GHL = angle MGH + angle LHD
=> angle AGM + angle MGH = angle GHL + angle LHD [from (3)]
=> angle AGH = angle GHD

therefore, AB || CD since angle AGH is equal to angle GHD [alternate angles]

Hence proved