Question

if ABCD is a rhombus then prove that 4 a b square equal to AC square + BD square​

Answer 1

step by step explanation

Answer 2

Given :  ABCD is a rhombus

To Find : prove that 4 AB² = AC² + BD²

Solution:

Property of rhombus

 Diagonal of rhombus bisects each other perpendicularly

and all sides of rhombus are equal

Let say Say side of Rhombus = a

AB = BC = CD = AD = a

and diagonal are d₁  & d₂

d₁  = AC

d₂ = BD

d₁  & d₂ bisect perpendicularly at O

Applying Pythagoras theorem

(d₁/2)² + (d₂/2)²   = a²

=> d₁²/4  + d₂²/4   = a²

Multiplying by 4 both sides

=>  d₁²  + d₂²   = 4a²

=> AC² + BD² = 4AB²

QED

Hence Proved

4 times the square of any side =  sum of squares of its diagonals

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