Question

11.Prove 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=90

o

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

o

.

Let us assume ∠A=90

o

Now,

AD∥BC[oppositesidesofaparallelogramareparallel]

And AB is transversal.

So, ∠A+∠B=180

0

[interioranglesonthwsamwsideofatransversalaresupplementary]

⇒90

o

+∠B=180

0

⇒∠B=90

o

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

∴∠C=∠A and ∠D=∠B

∴∠C=90

o

and ∠D=90

o

∴∠A=∠B=∠C=∠D=90

o

Hence, it is proved that ABCD is a rectangle.

Step-by-step explanation:

Answer 2

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sᴏʟᴜᴛɪᴏN:

• Let, ABCD be a rectangle.

Tᴏ ᴘʀᴏᴠᴇ:

• ∠A=∠B=∠C=∠D=90°

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

Let us assume ∠A=90°

Now,

AD∥BC[opposite sides of a parallelogram are parallel]

And AB is transversal.

So, ∠A+∠B=180 °

[interior angles on the same side of a transversal are supplementary]

⇒90 °+∠B=180 °

⇒∠B=90 °

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

∴∠C=∠A and ∠D=∠B

∴∠C=90 °

and ∠D=90 °

∴∠A=∠B=∠C=∠D=90°

Hence, it is proved that ABCD is a rectangle

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