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Question

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


A

Always Parallel

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B

Always Perpendicular

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C

Can be parallel or perpendicular

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D

Neither parallel nor perpendicular

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Solution

The correct option is A

Always Parallel


In a parallelogram, opposite angles are equal which means, A = C.

Then, 12 × DAC = 12 × ACB

Thus, EAC = ACF, which are alternate interior angles.

Hence, AE and CF are parallel lines.


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