In the following figure, verify that :
(i) $A C + B D = A D + B C$ (ii) $A B + C D = A D - B C$

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Solution

i) Now from the figure we've,
$A C + B D$
$= A C + (B C + C D)$ [ Since $B D = B C + C D$ ]
$= (A C + C D) + B C$
$= A D + B C$ .
So (i) is true.

ii) Again
$A D - B C$
$= (A B + B C + C D) - B C$ [ Since $A D = A B + B C + C D$ ]
$= A B + C D$ .
So (ii) is also true.

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