Question

Ac bd are diagnols abcd rhoumbs probe that ab2 +bc2+cd2+ad2=ac2+bd2

Answer 1

Answer:

In rhombus ABCD,

AB = BC = CD = DA

We know that diagonals of a rhombus bisect each other perpendicularly. That is

AC ⊥ BD, ∠AOB=∠BOC=∠COD=∠AOD=90°

and Consider right angled

triangle AOB, AB2 = OA2 + OB2 [By Pythagoras theorem]

⇒ 4AB2 = AC2+ BD2

⇒ AB2 + AB2 + AB2 + AB2 = AC2+ BD2 as we know AB=BC=CD=DA

∴ AB2 + BC2 + CD2 + DA2 = AC2+ BD2

Thus the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals.