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

To prove that quadrilateral ABCD is a parallelogram given the condition \(\vec{a} + \vec{c} = \vec{b} + \vec{d}\), we can follow these steps:

### Step 1: Rearranging the Given Equation
Start with the given equation:
\[ \vec{a} + \vec{c} = \vec{b} + \vec{d} \]
Rearranging this gives:
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