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Prove that the quadrilateral formed by j...

Prove that the quadrilateral formed by joining the mid-points of the sides of a square is also a square.

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Prove that the quadrilateral formed by joining the mid-points of the sides of a rectangle is a rhombus, but not a square.

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Knowledge Check

  • If each of sides of the square ABCD be a cm, then the length of each of the sides of the square, formed by joining the mid-points of the sides of ABCD is

    A
    `a/2 cm`
    B
    2a cm
    C
    `asqrt2` cm
    D
    `(asqrt2)/(2)cm`

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    Prove that the area of the parallelogram produced by joining the mid-points of the sides of a quadrilateral taken in order is half the area of the quadrilateral.

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    Using the properties of vectors, prove that the straight line, obtained by joining the mid-poings of two sides of a triangle , is half of the length of third side.

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    Prove that the line segment joining the mid-point of two transverse sides of a trapezium is parallel to its parallel sides.

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