ABCD is a quadrilateral in which AB=BC and AD=CD.Show that BC bisects both angles ABC and ADC
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In △ABD and △CBD,
AD=CD [ given ]
BD=BD [ Common ]
AB=BC [ given ]
Hence, △ABD≅△CBD [ SSS ]
∠ABD=∠1
∠CBD=∠2
∠1=∠2 [ CPCT ]
Also ,
∠3=∠4 [ CPCT ]
Hence ,
BD bisects both the angles ABC and ADE
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