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ABCD is a quadrilateral. P,Q,R, and s are the mid
Points of AB, BC, CD and DA respectively . Show
PR and QS bisects each other.

  • maths -

    After joining AC and using the midpoint of a triangle theorem ,it is easy to prove PQRS is a parallelogram

    A property of a parallelogram is that its diagonals bisect each other.
    Done.

    Write it up according to the method that your instructor wants.

  • maths -

    Hey can u explain me more briefly

  • maths -

    It is hard for me to tell how rigorous your proof must be.
    One of the features of Euclidean geometry is that it is cumulative, that is, you can use the result of one problem as a given in a new problem

    To reach this point illustrated by your problem above, you must have at one time proved that :
    In any triangle the line joining the midpoints of any two sides is one-half the length and parallel to the third side.
    As I said, I don't know whether your method would involve simply using that result, or whether you have to actually prove that as part of the above problem. I would guess you wouldn't have to.

    So you can prove that in PQRS , the opposite sides are parallel, thus making it a parallelogram.

    Then by drawing diagonals of this parallelogram, you can prove triangles congruent, ASA all over the place, and thus prove the diagonals bisect each other.
    (bisect means cutting into two equal parts)

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