rider of Pythagoras
Answers
Answered by
0
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
0Save
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).
Similar questions
Computer Science,
5 months ago
Social Sciences,
5 months ago
Science,
11 months ago
Science,
11 months ago