Question

In the given figure A, B, C, and D, E, F are two sets of collinear points, Then AD $\parallel$ CF.

• A. True
• B. False

Answer 1

The correct option is A

True

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) [Sum of opposite angles of a cyclic quadrilateral is ${180}^{\circ }$]

Also, 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

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

Therefore AD // CF ...... (co interior angles are supplementary)