# How to prove each angle of a rectangle as 90 degree.... without taking any angle as 90 degrees..

2
by HurricaneKartrina
u can c that all the lines are perpendicular to each other there
remembered me??
ya that only we have to prove
hmm i forgot it just i gave a clue

2015-03-19T23:18:11+05:30
The formula for finding the sum of the interior angles of any polygon is
(n-2) x 180 where n is the no. of sides the polygon has.
So the sum of the interior angles of a rectangle would be
(4-2) x 180
2 x 180 = 360 degrees
So the measure of one angle would be 360/4 (because there are four angles in a rectangle) = 90 degrees
Don't forget to thank me if it was helpful :)

u did not prove that all angles are equal
u didnt ask to prove that all angles are equal
then why did u divide by 4 without proving
2015-03-20T17:14:42+05:30
Consider a rectangle ABCD
join BD and AC
now,consider the triangle ABD and BAC
AB=AB (common)
AC=BD(diagonals of a rectangle are equal)
therefore,<A=<B (CPCT)....................................................(1)
now consider the triangle ABCD
as it is a parallelogram,the adjacent angles are supplementary
i.e.<A+<B=180.............................................................(2)
But,<A=<B
so, 2<A=180
<A=90
hence,<b=90 too'
llly,we can prove the rest.. :)
:)
:)
in order to prove each angle as 90, it should be a IIgm else u cant prove any random quad. as a rectangle with unequal diagonals
:)
as in this case, we use the property of equal diagonal of a parallelogram which bisect each other, so other way such a fig. formed has to be a parallelogram