Question

ABCD is a trapezium with AB || DC, the diagonals AC and BD are intersecting at E. If triangle AED is similar to Triangle BEC, then prove that AD =BC

Answer 1

They are not simular but equal areas.
ADD TRAINGLE AEB ON BOTH SIDES YOU GET


Area ABD = Area ACB AND AB//DC
SO CONVERSE OF THEORM YOU GET.

AB=DC

Answer 2

the triangles which are in same plane and between same parallel lines area are equal and those two triangles are equal angle aed and angle bec are equal because vertically opposite angles and AB and CD are parallel if BD is transversal angle dba and angle bdc are equal and if AC is transversal angle cab and angle acd are equal . finally by cpct property AD = BC