Prove that the quadrilateral formed by joining the mid-points of the pairs of consecutive sides of a quadrilateral is a parallelogram.

Explanation

To prove that the quadrilateral formed by joining the midpoints of the pairs of consecutive sides of a quadrilateral is a parallelogram, we will follow these steps:

### Step 1: Define the Quadrilateral and Midpoints
Let \( A \), \( B \), \( C \), and \( D \) be the vertices of the quadrilateral. The midpoints of the sides \( AB \), \( BC \), \( CD \), and \( DA \) are denoted as \( P \), \( Q \), \( R \), and \( S \) respectively.

### Step 2: Express the Midpoints in Vector Form
Using position vectors, we can express the midpoints as follows:
- \( P = \frac{\vec{A} + \vec{B}}{2} \) (midpoint of \( AB \))
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