With reference to the figure- ABCD is a parallelogram- AE and CF are angle bisectors of - D A C and - A C B respectively- What can you say about lines AE and CF-AA- Can be parallel or perpendicularB- Always ParallelC- Always PerpendicularD- Neither parallel nor perpendicular

You visited us 3 times! Enjoying our articles? Unlock Full Access!

Opposite Angles of a Parallelogram Are Equal

With referenc...

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?

Always Parallel

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Always Perpendicular

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Can be parallel or perpendicular

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Neither parallel nor perpendicular

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A
Always Parallel

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

Then, $\frac{1}{2}$ $\times$ $∠ D A C$ = $\frac{1}{2}$ $\times$ $∠ A C B$

Thus, $∠ E A C$ = $∠ A C F$ , which are alternate interior angles.

Hence, AE and CF are parallel lines.

Suggest Corrections

Similar questions

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 the lines AE and CF ?

ABCD is a parallelogram. AE and CF are angle bisectors of ∠DAC and ∠ACB, respectively. Show that the lines AE and CF are parallel to each other.

A B C D

is a parallelogram, and

A E

and

C F

bisects

∠ A

and

∠ C

respectively. Prove that

A E ∥ F C

In the adjacent figure, ABCD is a parallelogram and line segments AE and CF bisect the angles A and C respectively. Show that AE || CF.

Q. In the adjacent figure, ABCD is a parallelogram and the line segments AE and CF bisect the angles A and C respectively. Show that AE=CF

Join BYJU'S Learning Program

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?

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.