The bisectors of the angle of a parallelogram enclose a
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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