Question

In a rectangle ABCD, prove that :
AC² + BD² = AB² + BC² + CD² + DA²
​

Answer 1

To Prove:

AC² + BD² = AB² + BC² + CD² + DA²

Given:

A rectangle ABCD

Solution:

apply the formula of pythagorus theorem

in ∆ABC,

➙ AC² = AB² + BC²⠀......(1)

In ∆BAD,

➙ BD² = AB² + AD²⠀......(2)

Adding (1) and (2)

➙ AC² + BD² = AB² + BC² + BC² + DC²

Since,the given figure is rectangle,

⠀⠀⠀⠀⠀⠀➙ BC = AD

⠀⠀⠀⠀⠀⠀➙ BC² = AD²

Therefore,

AC² +BD² = AB² + BC² + BC² + DC²

➙ AB² + BC² + CD² + DA²

Thus,

LHS = RHS

Hence,

the given expression is proved.