Question

ABCD is a quadrilateral in which AB=BC and AD=CD show that BD bisects both the angles angle ABC and angle ADC​

Answer 1

Step-by-step explanation:

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