Q. 9

# The bisectors of the angle of a parallelogram enclose aA. ParallelogramB. RhombusC. RectangleD. Square

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 = 180o (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 = 90o 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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