Question

rider of Pythagoras​

Answer 1

Answer:

1. In the quadrilateral PQRS the diagonals PR and QS intersects at a right angle. Prove that PQ2+ RS2 = PS2 + QR2.

Diagonals are Intersects at a Right Angle

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Solution:

Let the diagonals intersect at O, the angle of intersection being a right angle.In the right-angle ∆POQ, PQ2 = OP2 + OQ2.

In the right-angle ∆ROS, RS2 = OR2 + OS2.

Therefore, PQ2 + RS2 = OP2 + OQ2 + OR2 + OS2 ................. (i)

In the right-angle ∆POS, PS2 = OP2 + OS2.

In the right-angle ∆QOR, QR2 = OQ2 + OR2.

Therefore, PS2 + QR2 = OP2 + OS2 + OQ2 + OR2 ................. (ii)

From (i) and (ii), PQ2+ RS2 = PS2 + QR2. (Proved).