# a rectangle must be square

• December 21st 2010, 06:56 AM
rcs
a rectangle must be square
I'm not really really good in geometry sorry need your help.

The points P
(0,0) , Q(a,0), R(a,b), S(0,b) are the vertices of the rectangle. Show that if the diagonals meet at right angles, then a = ± b and the rectangle must be a square.

Thanks.
• December 21st 2010, 07:28 AM
FernandoRevilla
$\overrightarrow{PR}\perp \overrightarrow{QS}\Leftrightarrow\overrightarrow{ PR}\cdot \overrightarrow{QS}\Leftrightarrow \ldots \Leftrightarrow -a^2+b^2=0$

http://www.fernandorevilla.es/