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Prove that bisectors of angles of …

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

    • Posted by Divyansh Chouhan 4 years, 10 months ago

    CBSE > Class 09 > Mathematics
    • 1 answers

    Yogita Ingle 4 years, 10 months ago


    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
       
    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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