Q. 9

# The bisectors of the angle of a parallelogram enclose a

A. Parallelogram

B. Rhombus

C. Rectangle

D. Square

Answer :

Let, ABCD is a parallelogram.

AE bisects ∠BAD and BF bisects ∠ABC

Also,

CG bisects ∠BCD and DH bisects ∠ADC

To prove: LKJI is a rectangle

Proof: ∠BAD + ∠ABC = 180^{o} (Because adjacent angles of a parallelogram are supplementary)

ΔABJ is a right triangle

Since its acute interior angles are complementary

Similarly,

In CDL, we get

∠DLC = 90°

In ADI, we get

∠AID = 90°

Then,

∠JIL = 90^{o} because ∠AID and ∠JIL are vertical opposite angles

Since three angles of quadrilateral LKJI are right angles, hence 4th angle is also a right angle

Thus LKJI is a rectangle.

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