Question

Show that each angle of a rectangle is a right angle?​

Answer 1

Answer:

Let, ABCD be a rectangle.

We have to prove that ∠A=∠B=∠C=∠D=90o

We know that a rectangle is parallelogram where its one angle is 90o.

Let us assume ∠A=90o

Now, 

AD∥BC[oppositesidesofaparallelogramareparallel]

And AB is transversal.

So, ∠A+∠B=1800[interior anglesonthwsamwsideofatransversalaresupplementary]⇒90o+∠B=1800⇒∠B=90o

Again, we know that opposite angles of a parallelogram are equal.

∴∠C=∠A and ∠D=∠B

∴∠C=90o and ∠D=90o

∴∠A=∠B=∠C=∠D=90o

Hence, it is proved that ABCD is a rectangle.