Question

in the figure a b is equal to bc and ac parallel BC prove that AB is equal to DC

Answer 1

As it is given that,
AD=BC and AD parallel to BC
hence ABCD is parallelogram
AB=DC (opposite sides of a parallelogram are equal )
hence proved

Answer 2

ad=bc
and angle bca = angle dac
angle dca= angle cab
so by angle angle side congruency
triangle abc = triangle dac
hence ab = dc