Q6 Prove that the sum of the squares of the diagonals of parallelogram is equal to the sum of the squares of its sides.
In parallelogram ABCD, AF and DE are altitudes drawn on DC and produced BA.
In DEA, by Pythagoras theorem
In DEB, by Pythagoras theorem
....................................2
In ADF, by Pythagoras theorem
In AFC, by Pythagoras theorem
Since ABCD is a parallelogram.
SO, AB=CD and BC=AD
In
(AE||DF)
AD=AD (common)
(ASA rule)
Adding 2 and, we get
(From 4 and 6)