Question

In figure A, B, C, and D, E, F are two sets of collinear points, Prove that AD $\parallel$ CF. [2 MARKS]

Answer 1

Concept: 1 Mark
Application: 1 Mark

In order to prove that AD $\parallel$ CF, it is sufficient to prove that

$\angle 1+\angle 3={180}^{\circ }$

Since ABED is a cyclic quadrilateral.

$\therefore$ $\angle 1+\angle 2={180}^{\circ }$ ....(i)

Now, BCFE is a cyclic quadrilateral and in a cyclic quadrilateral an exterior angle is equal to the opposite interior angle.

$\therefore$ $\angle 2=\angle 3$ ....(ii)

From equations (i) and (ii), we get

$\angle 1+\angle 3={180}^{\circ }$