Q. 34.5( 6 Votes )

In this figure a, b, c, d, e, f are two sets of collinear points. Prove that ad ll cf.

Answer :

The figure is given below:



In this figure, ABED is a cyclic quadrilateral.


DAB = BED ( as opposite angles of a cyclic quadrilateral are supplementary) ...(1)


BCFE is also a cyclic Quad.


BCF = BEF(as opposite angles of a cyclic quadrilateral are supplementary)…(2)


when we add these angles


DAB + BED + BCF + BEF = 360°…(1)


BED + BEF = 180°


DAB + BCF = 180°


But they are co-interior angles and if co-interior angles sum up to 180° they are parallel.


So AD parallel to CF.


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