In the figure, B and E are points on line segment AC and DF respectively. Prove that AD||CF.
Join B and E.
ABED is a cyclic quadrilateral.
ADE = EBC … (1)
(exterior angle of a cyclic quadrilateral = Interior opposite angle)
Similarly, EFCB is a cyclic quadrilateral.
EBC + CFE = 180o … (2)
(opposite angles of a cyclic quadrilateral are supplementary)
From (1) and (2),
ADE + CFE = 180o
But these are interior angles made by the transversal DF on the same side of the lines AD and CF. Since, these angles are supplementary, therefore,
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