Question

show that each angle of a rectangle is a right angle

Answer 1

Solution:-

Let us consider a rectangle ABCD.

We know that the diagonals of a rectangle are equal. Therefore, AC = DB

In triangle ABC and triangle DCB,

AB = DC (Opposite sides of a parallelogram)

AC = DB

BC = CB (Common side)

Therefore, triangle ABC is congruent to triangle DCB.

And, angle ABC = angle DCB (CPCT)

And, angle ABC + angle DCB = 180° (Adjacent angles of a parallelogram are supplementary/Co interior angles)

Therefore, angle ABC = angle DCB = 90°

And, angle ABC = angle ADC = 90° and angle DCB = angle BAC = 90° (Opposite angles of a parallelogram are equal.)

Hence, each angle of a rectangle measures 90°

Hence proved.

please brainliest

Answer 2

Heyy
here is your answer

see above image
opposite sides are congruent

now we know
sum of all angles is 360°

let every angle be x
4(x) =360°
x=360°/4
x=90°