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


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


In CDL, we get

DLC = 90°

In ADI, we get

AID = 90°


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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