# ABCD is a quadrilateral. Show that vec(AB)+vec(AD)+vec(CB)+vec(CD)=4vec(PQ) where P and Q are the mid points of AC and BD respectively?

Mar 14, 2018

That's true

#### Explanation:

https://www.geogebra.org/m/WgaNJ5Xq

$\setminus \vec{A B} + \setminus \vec{A D} = 2 \setminus \cdot \setminus \vec{A Q}$
$\setminus \vec{A B} + \setminus \vec{B C} = 2 \setminus \cdot \setminus \vec{A P}$
$\setminus \vec{P Q} = \setminus \vec{A Q} - \setminus \vec{A P}$

$2 \cdot \setminus \vec{P Q} = \setminus \vec{A D} + \setminus \vec{C B}$
$2 \cdot \setminus \vec{P Q} = \setminus \vec{A B} + \setminus \vec{C D}$