Question

Prove that Each angle of a rectangle is a right angle. ​

Answer 1

Solution :

Let ABCD be a rectangle such that $\angle\: A$ = 90°.

Since ABCD is a parallelogram.

$\therefore \sf AB = DC,BC = AD \:$

$\angle \sf \: A = B = C = D$

Now,AB || DC and AD intersects them at A and D

$\therefore \: \angle \sf \: A + \angle \: D = {180}^{o}$

$\sf \implies {90}^{o} + \angle \: D = {180}^{o}$

$\sf \implies \angle D = {180}^{o} - {90}^{o}$

$\sf \implies \angle D = \large \boxed{ \sf \: {90}^{o}}$

Here, Angle B is equal to the Angle D

$\sf \therefore \: \angle B= \large \boxed{ \sf \: {90}^{o}}$

Hence,

$\angle \sf \: A = B = C = D = {90}^{o}$

Answer 2

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