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

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)

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.

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