Question

Prove that:-<br />Using opposite Angles test for paralleogram, prove that every rectangle is paralleogram

Answer 1

Answer:

Properties of a Parallelogram:

• Opposite angles are equal.
• Adjacent angles are supplementary.
• Opposite sides are parallel

For diagram refer attachment.

Consider a Rectangle ABCD.  

Here,

• ∠A and ∠C are opposite angles along with ∠B and ∠C which are also opposite angles.
• ∠A is adjacent to ∠B and ∠C is adjacent to ∠D

⇒ ∠ A = ∠ C = 90° ; ∠ B = ∠ D = 90°

⇒ ∠ A + ∠ B = 90° + 90° = 180° ; ∠ C + ∠ D = 90° + 90° = 180°

Hence opposite angles are equal as well as adjacent angles are supplementary.

Hence we can say that every rectangle is a parallelogram.

Hence proved !!