Question

ABCD is a quadrilatral in which AD=BC and angleDAB=angleCAB prove that

Answer 1

lets take ΔABD and ΔADC

So,
AB=AC  [given]
BD=DC  [the transversal divides the base into two equal halfs]
AD=AD   [common]

so,ΔABD≈ΔADC

So ,
by C.P.CT    ∠DAB = ∠CAB  - proved !