Question

Show that if the diagonals of a quadrilateral
cut each other in a right angle, then the sum of
the squares of opposite sides are equal.​

Answer 1

Step-by-step explanation:

Hey mate... It's easy!

Let the quadrilateral be ABCD

Now,

By pythagoras theorem,

AB2= AO2+OB2..... (1)

Also,

CD2=CO2+OD2...... (2)( AB and CD are opposite sides)

Now,

AD2=AO2+OD2... (3)

And

BC2=BO2+OC2....(4) (AD and BC are opposite sides)

By adding (1) and (2)

We get

AB2+ CD2=AO2+OB2+CO2+OD2

Also by adding (3) and (4),

We get the same answer.

Hence proved

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