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The bisectors of the angle of a parallelogram enclose a-A) ParallelogramB) RhombusC) RectangleD) Square |
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Answer» RECTANGLE............ Given: ABCD is a parallelogram. AE bisects ∠BAD. BF bisects ∠ABC. CG bisects ∠BCD and DH bisects ∠ADC To prove: LKJI is a rectangle ∠BAD + ∠ABC = 180° because adjacent ANGLES of a parallelogram are supplementary [Since SUM of adjacent angles of a parallelogram are supplementary] ΔABJ is a RIGHT triangle since its acute interior angles are complementary Similar in ΔCDL we get ∠DLC = 90° and in ΔADI we get ∠AID = 90° Then ∠JIL = 90° as ∠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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