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In the figure, B and E are points on line segment AC and DF respectively. Prove that AD||CF.

Asked by Topperlearning User 4th June 2014, 1:23 PM
Answered by Expert
Answer:

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,

AD||CF

Answered by Expert 4th June 2014, 3:23 PM
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