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

Question

In
the given figure GM and HL are bisectors of
∠𝐴𝐺𝐻
and∠𝐺𝐻𝐷
respectively such that GM∥HL Show that AB ∥ CD

Atul Shaw · Accepted Answer

Dear student,
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 [GMIIHL]------(3)
Adding (1), (2)
angle ( AGM+GHL)= angle (MGH+LHD)
angle (AGM+MGH)= angle(GHL+LHD)------ from(3)
angle AGH= angle DHG
Therefore, ABllCD since angle AGH=angle DHG (alternate angle)
Hence proved
Regards

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

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