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

Answer and Step-by-step explanation in the attachment.

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Answer 2

Answer:

let the Quadrilateral be ABCD

Now ,

By Pythagoras theorem

Step-by-step explanation:

AB^=AO^+OB^------(1)

Also ,

CD^=CO^+OD^------(2) (AB and BC are opposites sides)

Now ,

AD^=AO^+OD^------(3)

and ,

BC^=BO^+OC^------(4) ( Ad and BC are opposites sides)

By adding (1) and (2)

We get ,

AB^+CD^=Ao^+OB^+CO^+OD^

HENCE PROVED