ABCD and ABXY are two parallelograms on the same base AB on opposite sides of it.Prove that XCDY is alsoa parallelogram.

Question

ABCD and ABXY are two parallelograms on the same base AB on
opposite sides of it Prove that XCDY is alsoa parallelogram

S. Usha Rani · Accepted Answer

Join YD and AC
Given ABCD is a parallelogram
So, AB=CD and AB||CD (1)
Also, ABXY is a parallelogram
AB=XY and AB||XY (2)

From (1) and (2),
CD=XY and CD||XY (transitive property)
So, XCDY is a parallelogram