If the non parallel sides of a trapezium are equal.prove it is cyclic

1.	If the non parallel sides of a trapezium are equal.prove it is cyclic
Answer» Given - AB \|\| CD , AD = BC T.P. - ABCD is a cyclic Construction - BE \|\| AD Proof - Here AB\|\|CD & AD = BC ABED is a parallelogram => BAD = BED - 1 eq.Also AD =BC = BE Therefore ,. BE = BC Angle BEC = angle BCE - 2 eq. Now, angle BED + angle BEC = 180 ( L.P. ) angle BAC + angle BCE = 180 ( from 1 & 2eq. ) angle A + angle C = 180 Therefore ,. ABCD is a cyclic.

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