Question

Here is the printed one

Answer 1

As there is a right angle at T, all the 4 triangles are right angled at T. By geometry, we can see that all the sides of the quadrilateral are the hypotenuse of the triangles.

Now, PQ^2=PT^2+QT^2
SR^2=ST^2+RT^2
Adding them both, we get,
PQ^2+SR^2=PT^2+QT^2+ST^2+RT^2.

Now, QR^2=QT^2+RT^2
PS^2=PT^2+ST^2
Adding them both, we get,
QR^2+PS^2=PT^2+QT^2+ST^2+RT^2.

THEREFORE, PQ^2+QR^2=SR^2+PS^2

Q. E. D.