Question

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?

Answer 1

That's true

Explanation:

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

`\vec (AB)+\vec (AD)= 2 \cdot \vec (AQ)`
`\vec (AB)+\vec (BC)= 2 \cdot \vec (AP)`
`\vec (PQ)=\vec (AQ)- \vec (AP)`

`2 cdot \vec(PQ)=\vec (AD)+\vec(CB)`
`2 cdot \vec(PQ)=\vec (AB)+\vec(CD)`