Prove that bisectors of angles of a parallelogram forms a rectangle.

1.	Prove that bisectors of angles of a parallelogram forms a rectangle.
Answer» Given: ABCD is a parallelogram. AE bisects ∠BAD. BF bisects ∠ABC. CG bisects ∠BCD and DH bisects ∠ADCTo prove: LKJI is a rectangle∠BAD + ∠ABC = 180° because adjacent angles of a parallelogram are supplementary\xa0ΔABJ is a right triangle since its acute interior angles are complementarySimilar in ΔCDL we get ∠DLC = 90° and in ΔADI we get ∠AID = 90°Then ∠JIL = 90° as ∠AID and ∠JIL are vertical opposite anglesSince three angles of quadrilateral LKJI are right angles, hence 4th angle is also a right angle.Thus LKJI is a rectangle.\xa0 \xa0 \xa0

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