Question

∆PQR is an isosceles triangle ,right angled at R . prove that PQ^2=2PR^2

Answer 1

$\textsf{Given:}$

$\mathsf{\triangle\,PQR\;}\textsf{ is an isocceles right angled triangle at R }$

$\textsf{Then, by Pythagoras theorem}$

$\mathsf{PQ^2=PR^2+QR^2}$

$\textsf{since PQR is an isoceles triangle, we have PR=QR}$

$\implies\mathsf{PQ^2=PR^2+PR^2}$

$\implies\boxed{\mathsf{PQ^2=2\,PR^2}}$