Question

The diagonals of a square are ABCDmeet at O. Prove that AB^2=2AO^2

Answer 1

Answer:

let ABCD be the square whose diagonals meet at O

take one right angled triangle AOB

applying pythagoras theorem in ∆AOB

AB^2 = OA^2 + OB^2

as OA=OB

AB^2= OA^2 +OA^2

AB^2 = 2OA^2..

hence proved