Question

Prove that all rectangle are 90°each.

Answer 1

A rectangle is defined to be an "equiangular parallelogram". So a rectangle is any four-sided polygon, having two pairs of parallel opposite sides, and four angles which are equal in measure. With this definition, we must still "prove" that each angle measures 90 degrees

Answer 2

Heya,

here is your answer,
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Consider the following figure of rectangle . ( Refer the pic )

The diagonals AC and BD intersect at O.

Thus the vertical angles - angle AOD = angle BOC

Since the line segments AB and CD are parallel lines, and AC is the transversal, then the alternate interior angles

=> angle OCB = angle OAD

Since the line segments AB and CD are parallel lines, and BD is the transversal, then the alternate interior angles

=> angle OBC = angle ODA

The sides AD = BC

Therefore, by Angle-Side-Angle congruence, 

=> triangle AOD = triangle BOC

AB and CD are parallel, and BD is a transversal, therefore, the angles

=> angle CDB = angle ABD

Now, Angle ADC = angle ODA + angle BDC
And, Angle ABC = angle OBC + angle ABD

●Thus, Angle ADC = angle ABC

We also know that in a parallelogram, the sum of opposite angles are 180 degrees.

Also , Angle ADC + angle ABC = 180°

Since angle ADC = angle ABC , they have to be equal to 90 degrees each.

Thus, in a rectangle all the angles are 90 degrees.

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Hope it helps u !!!

Cheers ☺☺

# Nikky