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9th Class Mathematics Quadrilaterals Question Bank Quadrilaterals

  • question_answer
    X, Y are the mid-points of opposite sides AB and DC of a parallelogram ABCD. AY and DX are joined intersecting in S; CX and BY are joined intersecting in R. Then SXRY is a

    A)  Rectangle         

    B)         Rhombus                     

    C)         Parallelogram               

    D)         Square 

    Correct Answer: C

    Solution :

    In quadrilateral AXCY, \[AX||CY\]                    (\[\because \]\[AB||CD\])    ?(i) \[AX=\frac{1}{2}AB\]and \[CY=\frac{1}{2}CD\] (\[\therefore \]X and Y are midpoint of AB and CD) Also, AB = CD (Opposite sides of parallelogram) So, \[AX=CY\] \[\Rightarrow \]AXCY is a parallelogram (from (i) and (ii)) Similarly, quadrilateral DXBY is a parallelogram. In quadrilateral SXRY, \[SX||YR\] (\[\because \]SX is a part of DX and YR is a part of YB) Similarly, \[SY||XR\] So, SXRY is a parallelogram.


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