Question

In the given figure, the diagonal of a quadrilateral PQRS are intersected at T at right angle. prove that PQ^2 + SR^2 = QR^2 + PS ^2

Answer 1

since diagonals bisect at right angles,
ST^2+RT^2=SR^2 (Pythagoras theorem)
similarly,
RT^2+QT^2=QR^2
QT^2+PT^2=PQ^2
PT^2+ST^2=PS^2

adding PQ^2 and SR^2
=QT^2+PT^2+ST^2+RT^2
=(RT^2+QT^2)+(PT^2+ST^2)
=QR^2+PS^2

Hence proved.