**·**2013-10-10 08:46:25

Let the 4 vertices be \vec{A},\vec{B},\vec{C},\vec{D}.

The mid-point of the sides \frac{\vec{A}+\vec{B}}{2},\frac{\vec{C}+\vec{D}}{2},\frac{\vec{A}+\vec{D}}{2},\frac{\vec{B}+\vec{C}}{2}

Mid-point of the line joining the mid-points of side AB and CD=\frac{\vec{A}+\vec{B}+\vec{C}+\vec{D}}{4}

Mid-point of the line joining the mid-points of side BC and DA=\frac{\vec{A}+\vec{B}+\vec{C}+\vec{D}}{4}

Similarly the mid-point of the line joining the mid-points of the diagonals = \frac{\vec{A}+\vec{B}+\vec{C}+\vec{D}}{4}

Hence they all meet at a point and bisect each other.