Consider a rectangle ABCD, then: $A C^{2} + B D^{2} = A C^{2} + B C^{2} + C D^{2} + D A^{2}$ .
If the above statement is true then mention answer as 1, else mention 0 if false

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Solution

Given: ABCD is a rectangle.
Join AC and BD.
Now, In $△ A B C$ ,
$A C^{2} = A B^{2} + B C^{2}$ (I) (By Pythagoras theorem)
Similarly, In $△ A B D$ ,
$B D^{2} = A D^{2} + A B^{2}$ (II) (By Pythagoras theorem)
Similarly, In $△ B D C$ ,
$B D^{2} = B C^{2} + C D^{2}$ (III) (By Pythagoras theorem)
Similarly, In $△ A C D$ ,
$A C^{2} = A D^{2} + C D^{2}$ (IV) (By Pythagoras theorem)
Adding I, II, III, IV
$2 (A C^{2} + B D^{2}) = 2 (A B^{2} + B C^{2} + C D^{2} + A D^{2})$
$A C^{2} + B D^{2} = A B^{2} + B C^{2} + C D^{2} + A D^{2}$

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