Question

in a quadrilateral the greatest and the smallest sides are opposite to each other. Prove that the adjacent angle to the greatest side is smaller than its opposite side. ​

Answer 1

Answer:Given:

In quadrilateral ABCD, AB smallest & CD is longest sides.

To Prove: ∠A>∠C

& ∠B>∠D

Construction: Join AC.

Mark the angles as shown in the figure..

Proof:

In △ABC , AB is the shortest side.

BC > AB

∠2>∠4 …(i)

[Angle opposite to longer side is greater]

In △ADC , CD is the longest side

CD > AD

∠1>∠3 …(ii)

[Angle opposite to longer side is greater]

Adding (i) and (ii), we have

∠2+∠1>∠4+∠3

⇒∠A>∠C

Similarly, by joining BD, we can prove that

∠B>∠D

hope it helps u

Step-by-step explanation: