In a quadrilateral ABCD ,which is not a trapezium.It is known that <DAB=<ABC=60 DEGREE.moreover , <CAB=<CBD.Then A) AB=BC+CD B) AB=AD+CD C) AB=BC+AD D) AB=AC+AD ? Choose correct option.

Option( c)is correct

i.e.AB=BC+AD

Given

• ##"In quadrilateral "ABCD, /_DAB=/_ABC=60^@##

• ##/_CAB=/_CBD##

Construction

• ## BC and AD " are produced to intersect at E"##

• ## In Delta ABE,/_EBA=/_EAB=60^@ =>/_BEA=60^@##

• ##:. Delta ABE " is equilateral"->AB=BE=EA##

Now

• ##In DeltaABC and Delta BED, /_BED=/_CBA=60^@## ##/_EBD=/_CAB (given)and BE= AB (proved)##
• ## DeltaABC and Delta BED " are congruent by ASA Rule"##
• ##:.DE = BC " corresponding sides"## ##"of congruent triangles"##
• ## "Finally", AB=AE=AD+DE=AD+BC##

So option (c) is correct