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If the diagonals of a parallelogram are perpendicular, then it is a rhombus.

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Write the following statements in symbolic form and write their negatins : (1) Mangoes are delicious, but expensive. (2) A person is rich if and only if he is a software engineer. (3) If diagonals of a parallelogram are perpendicular, then it is a rhombus. solution :

Consider the following statements : 1. If the diagonals of a parallelogram ABCD are perpendicular , then ABCD may be a rhombus. 2. If the diagonals of a quadrilateral ABCD are equal and perpendicular , then ABCD is a square. Which of the statements given above is/are correct ?

Knowledge Check

  • The diagonals of a rhombus

    A
    are always equal
    B
    never bisect each other
    C
    always bisect each other at an acute angle
    D
    always bisect each other at right angles

  • One diagonal of a parallelogram is 40 cm and the perpendicular distance of this diagonal from either of the outlying vertices is 19 cm. The area of the parallelogram (in sq cm) is

    A
    700 `cm^(2)`
    B
    380 `cm^(2)`
    C
    760 `cm^(2)`
    D
    1140 `cm^(2)`

  • If the diagonals of a rhombus are equal, then the rhombus is a:

    A
    parallelogram but not a square
    B
    parallelogram but not a rectangle
    C
    rectangle but not a square
    D
    square

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    if diagonals of a parallelogram bisect each other,prove that its a rhombus

    Using analytical geometry,prove that the diagonals of a rhombus are perpendicular to each other.

    Show that the diagonals of a rhombus are perpendicular to each other

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