Answer :
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
⇒ 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
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