Question

show that each angle of a rectangle is a right angle

Answer 1

Given : A rectangle ABCD, such that ∠A = 90 0

Prove that : ∠A = ∠B = ∠C = ∠D = 90 0
Statements Reasons

1) ABCD is a rectangle. 1) Given
2)∴ ABCD is a Parallelogram. 2) Every rectangle is a Parallelogram.
3) AD || BC 3) By Properties of parallelogram.
4) ∠A + ∠B = 1800 4) Interior angles on the same side of transversal are supplementary.
5) 90 + ∠B = 180 5) ∠A = 90 (Given)
6) ∠B = 900 6) By subtraction property.
7) ∠D= 90 and ∠C= 90 7) By properties of parallelogram.

Answer 2

in general, for all polygons except for some quadrilaterals, if sides are equal
then all angles are equal
this is generally termed as regular polygon
but in case of rectangle,both pairs of parallel sides are equal
we won't find a regular rectangle
if it is regular it is square,not rectangle
so,rectangle is a special case
let us take a rectangle ABCD
IN GENERAL FOR A POLYGON OF FOUR SIDES THE SUM of angles will be 360
I.e,by n(n+1)/2
so if take AB=X,BC=Y
THEN CD=X,AD=Y

BY EUCLID'S TWO LINES DRAWN FROM TWO POINTS ARE ENDED WITH TWO POINTS OF ANOTHER LINE OF LENGTH
IN THIS CASE PARALLEL SIDES ARE EQUAL AND EACH ANGLE SHOULD BE A QUARTER OF COMPLETE ANGLE


HOPE HELPED