Question

With reference to the figure, ABCD is a parallelogram. AE and CF are angle bisectors of ∠DAC and ∠ACB respectively. What can be said about lines AE and CF?

• A. Always parallel
• B. Always perpendicular
• C. Can be parallel or perpendicular
• D. Neither parallel nor perpendicular

Answer 1

The correct option is A

Always parallel

AC is a diagonal of the parallelogram ABCD. Now, $\angle$DAC = $\angle$ACB (Alternate angles)

$\Rightarrow \frac{1}{2}\times$ $\angle$DAC = $\frac{1}{2}\times$ $\angle$ACB
$\Rightarrow \angle EAC=\angle ACF$ ($\because \frac{1}{2}\times$ $\angle$DAC = $\angle EAC$ and $\frac{1}{2}\times$ $\angle$ACB = $\angle ACF$)

Hence, AE and CF are parallel lines.