Using vector method, prove that the line segments joining the mid-points of the adjacent sides of a quadrilateral taken in order form a parallelogram.

Explanation

To prove that the line segments joining the mid-points of the adjacent sides of a quadrilateral form a parallelogram using vector methods, we can follow these steps:

### Step 1: Define the Quadrilateral and Midpoints
Let the vertices of the quadrilateral be represented by the position vectors:
- \( \vec{A} \) for point A
- \( \vec{B} \) for point B
- \( \vec{C} \) for point C
- \( \vec{D} \) for point D
...