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In the given figure, $GH$ is parallel to $NO$. $NR$ bisects $\angle MNO$ and $OR$ bisects $\angle MON$. Show $GH=NG+OH$.
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Given: $GH || NO$  , $NR$ bisects $\angle MNO$ and $OR$ bisects $\angle MON$.

To do: To prove that $GH =NG+OH$

Solution:

$GH || NO$

$\angle GRN = \angle ONR$  ( alternate angle)

$\angle GNO = \angle MNO$  as $G$ is on line $MN$

$\angle GNR =\angle ONR$  as  $NR$ bisects $\angle MNO$

$\Rightarrow \angle GRN = \angle GNR$

$\Rightarrow GN = GR$

Similarly

$\angle NOR = \angle HRO$

$\angle NOR = \angle HOR$  as  $OR$ bisects $\angle MON$

$\Rightarrow \angle HRO =\angle HOR$

$\Rightarrow OH=HR$

$GN + OH = GR + HR$

$\Rightarrow GN + OH = GH$

Hence Proved
 

Updated on: 10-Oct-2022

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