If `veca, vecb, vecc, vecd` are the position vectors of points `A, B, C and D`, respectively referred to the same origin O such that no three of these points are collinear and `veca+vecc=vecb+vecd`, then prove that quadrilateral `ABCD` is a parallelogram.

Explanation

Since `veca+vecc=vecb+vecd`, we have
`" "(veca+vecc)/(2)=(vecb+vecd)/(2)`
i.e., Midpoint of `AC` and `BD` coincide.
Hence, quadrilateral `ABCD` is a parallelogram.