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 = 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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