Question

if a pair of opposite sides of a cyclic quadrilateral are equal, then prove that the other two sides are parallel

Answer 1

GIVEN :-

⇒ ABCD is a cyclic quadrilateral.

⇒ And AD = BC


CONSTRUCTION :-

⇒ Let us join BD.


TO PROVE :-

⇒ AB  | | CD


PROOF :-

In cyclic quad ABCD,

                           ⇒ AD  = BC { Given }
                       

                           ⇒∠1 = ∠2    {Remember the theorem Equal chords                                              subtend equal angles at the circumference of the circle]
                           

                           ⇒ Arc DA = Arc BC { Because it is given that  AD = BC}

And also angle 1 and 2 are the alternate interior angles because it lie on the parallel lines AB and CD on transversal  BD.

So  AB is parallel  to CD