Question

in the given figure gh is parallel to no.nr bisects angle mno and or bisects angle mon.show that gh =ng+oh​

Answer 1

Given : GH || NO  , NR bisects angle MNO and or bisects angle mon.

To Find : show that GH =NG+OH

Solution:

GH || NO

∠GRN = ∠ONR  ( alternate angle)

∠GNO = ∠MNO  as G is on line MN

∠GNR = ∠ONR  as  NR bisects ∠MNO

=> ∠GRN = ∠GNR

=> GN = GR

Similarly

∠NOR = ∠HRO

∠NOR = ∠HOR  as  OR bisects ∠MON

=> ∠HRO =  ∠HOR

=> OH =HR

GN + OH = GR + HR

=> GN + OH = GH

QED

Hence Proved

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