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Math Help - Parallelogram Help

  1. #1
    Junior Member whytechocolate01's Avatar
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    Post Parallelogram Help

    Prove: If a diagonal of a parallelogram bisects an angle of the parallelogram, the parallelogram is a rhombus. State your plan and give proof.

    Given: ABCD is a parallelogram with angle 1 congruent to angle 2.
    To Prove: ABCD is a rhombus
    Plan: _________________________________________________

    PROOF

    Statements:__________________________________


    Reasons: _____________________________________
    Attached Thumbnails Attached Thumbnails Parallelogram Help-abca.jpg  
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  2. #2
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    Hello, whytechocolate!

    I'll give you the game plan . . . you fill in the details.


    Prove: If a diagonal of a parallelogram bisects an angle of the parallelogram,
    the parallelogram is a rhombus.
    We know that: .AB = CD, AD = BC .(Opposite sides of a parallelogram are equal)

    We need to show that two adjacent sides are equal: say, AB = BC.


    We know that: .angle A = angle C. .
    (Opposite angles of a parallelogram are equal)

    AC bisects angles A and C.
    . . Hence: /1 = /2 = /3

    Since /2 = /3, triangle ABC is isosceles.

    Therefore: .AB = BC

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