# Please help sum 12(I)

Let

*ABCD*be a rectangle.

Here,

*AB*=

*CD*and

*BC*=

*DA and*∠

*A*

*=*∠

*B*

*=*∠

*C*

*=*∠

*D*

*=*90

^{o}

Now, we have:

∠

*ABD*= ∠

*DBC*[ ∵

*BD*bisects ∠

*B*

*]*

∠ADB = ∠

*DBC*[ Alternate interior angles]

∠

*ABD*= ∠

*ADB*

As the two opposite angles of ∆

*ABD*

*are equal, the opposite sides must also be equal.*

i.e.,

*AB*=

*DA*

∴

*AB*=

*CD*=

*DA = BC*

So, when all the sides are equal and all the angles are of 90

^{o}, the quadrilateral is a square.

Hence,

*ABCD*is a square.

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