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## Answers

As the quadrilateral is a rectangle

a+d=b+c

∴ a=b+c-d-----------------------------------(1)

From the above reason

a+b=c+d

from (1)

b+c-d+b=c+d

⇒ 2b=2d

⇒ b=d-----------------------------------------(2)

Substituting from (2) in (1)

a+d=c+d

⇒ a=c------------------------------------------(3)

From (2) and (3)

a+d = a+b-----------------------------------(4)

Similarly we can prove that

a+b=b+c-----------------------------------(5)

and b+c=c+d------------------------------------(6)

and c+d=a+d------------------------------------(7)

From (4) , (5) , (6) and (7) we can prove that the rectangle is a square.