# Thread: Vector Proof Problem

1. ## Vector Proof Problem

'Let ABCD be a quadrilateral in the plane, and let P and Q be the midpoints of of the sides AB and CD respectively. Show that:

2PQ = AD + BC'

I'm just not sure how to go about it. Thanks in advance for any help.

2. Originally Posted by AlanC877
Let ABCD be a quadrilateral in the plane, and let P and Q be the midpoints of of the sides AB and CD respectively. Show that: 2PQ = AD + BC'
$\[\frac{1}{2}\overrightarrow {AB} + \overrightarrow {BC} + \frac{1}{2}\overrightarrow {CD} = \overrightarrow {QP}$

$- \frac{1}{2}\overrightarrow {AB} + \overrightarrow {AD} - \frac{1}{2}\overrightarrow {CD} = \overrightarrow {QP}$

Now add those together.

3. Thanks very much, now I realise just how easy the question actually was!