Question

To prove that the sum of the squares of the diagonals of parallelogram is equal to the sum of the squares of its sides

Answer 1

Answer:

Step-by-step explanation:

please draw one parallelogram ABCD with diagonal with centre O

Given : ABCD is a parallelogram,AB=BC=CD=DA=x

To prove:AB Square+BC Square+CD Square+DA Square=AC Square+BD Square

Proof:We know in a parallelogram diagonals bisect each other at right angle

so,AC perpendicular BD

OA=OC,OB=OD

OA=OC=Half if AC,OB=OD=BD by 2

In right angled triangle AOB

using pythagoras theorem

AB Square=OA Square+OB Square

x square=AC by 2 square+BD by 2 square

x square=AC by 4 square +BD by 4 square

x square=AC Square+BD Square by 4

4x square=AC square+BD Square

so,AB Square+BC Square+CD square+DA square=AC Square+BD Square

hence proved