Question
Show that each angle of a rectangle is a right angle.
✓
Answer
We know that rectangle is a parallelogram whose one angle is right angle.
Let ABCD be a rectangle. $\angle A = {90^0}$
To prove $\angle B = \angle C = \angle D = {90^0}$
Proof: $\because AD\parallel BC$ and AB is transversal
$\therefore \angle A + \angle B = {180^0}$
${90^0} + \angle B = {180^0}$
$\angle B = {180^0} - {90^0} = {90^0}$
$\angle C = \angle A$
$\therefore {\text{ }}\angle C = {90^0}$
$\angle D = \angle B$
$\therefore {\text{ }}\angle D = {90^0}$
Hence, all the angles of the rectangles is a right angle.
Let ABCD be a rectangle. $\angle A = {90^0}$
To prove $\angle B = \angle C = \angle D = {90^0}$
Proof: $\because AD\parallel BC$ and AB is transversal
$\therefore \angle A + \angle B = {180^0}$
${90^0} + \angle B = {180^0}$
$\angle B = {180^0} - {90^0} = {90^0}$
$\angle C = \angle A$
$\therefore {\text{ }}\angle C = {90^0}$
$\angle D = \angle B$
$\therefore {\text{ }}\angle D = {90^0}$
Hence, all the angles of the rectangles is a right angle.
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