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given ,
AB = CD
angle ABM = angle CDN
here ,
ABM + ABO = 180⁰ ( linear pair ) --------> ( 1 )
CDN + CDO = 180⁰ ( linear pair ) --------> ( 2 )
therefore ,
( 1 ) , ( 2 ) = ABO = CDO
again ,
angle AOB = angle COD ( vertically opposite angle )
therefore ,
∆ AOB ≡ ∆ COD ( AAS congruency )
proved
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