Question

The bisectors of the angle of a parallelogram enclose a : 

A. Parallelogram 

B. Rhombus 

C. Rectangle 

D. Square

Answer 1

Option : (C)

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°

(Because adjacent angles of a parallelogram are supplementary) 

ΔABJ is a right triangle 

Since, 

its acute interior angles are complementary 

Similarly, 

In ΔCDL, we get 

∠DLC = 90° 

In ΔADI, we get

∠AID = 90°

Then, 

∠JIL = 90° because ∠AID and ∠JIL are vertical opposite angles 

Since, 

Three angles of quadrilateral LKJI are right angles, 

Hence,

4^th angle is also a right angle

Thus,

LKJI is a rectangle.