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Home >> Square >> Diagonals of Square >>

Diagonals of Square

Area of square Perimeter of Square Diagonals of Square Construction of Square with Compass

There are three properties of square

  • Diagonals of Square are equal
  • Diagonals of Square bisect each other
  • Diagonals of Square are perpendicular bisector of each other

    Diagonals of Square are equal

    This property explains that length of diagonals of a square is equal
    So, if we know the length of one diagonal, length of other can be calculated.

    Example 1: In the following diagram of square ABCD, diagonal AC = 5 cm. Find length of other diagonal BD ?



    Solution: In the given square ABCD:
    AC = 9 cm (given)

    Since, diagonals in rectangle are equal, so we get:
    AC = BD

    Put Value of AC (given) and we get:
    9 cm = BD

    Or we can write it as
    BD = 9 cm

    Hence, length of other diagonal BD is 9 cm

    Diagonals of Square bisect each other

    This property explains that diagonals of square bisect each other at the intersecting point.
    In simple words, we can say that:
    Diagonals of square divide into half at the point of intersection

    Example 2: Observe the following diagram:



    In the above diagram of Square ABCD:
    AC and DB are two diagonals
    AC = DB = 15 cm

    Both diagonals AC and DB intersect at point O
    Since the diagonals of parallelogram bisect each other at the intersecting point, so we get:
    AO = OC = Half of AC
    Since AC = 15 cm, so we get
    AO = OC = 7.5 cm

    Similarly,
    DO = OB = 7.5 cm

    Diagonals of Square are perpendicular bisector of each other

    This property of square explains that diagonals of square bisect each other and make an angle of 90 degree; at the point of intersection.

    Example 3: Observe the following diagram:



    In the above diagram of square ABCD:
    AC and BD are diagonals which intersect at point O and we get:

    AO = OC & DO = OB because diagonals of square bisects each other --------(statement 1)

    Also we get:
    Angle 1 = Angle 2 = Angle 3 = Angle 4 = 90 degree each --- because diagonals of square are perpendicular to each other at point of intersection -------------(Statement 2)

    Put together statement 1 and 2 & we say that:
    Diagonals of Square are perpendicular bisector of each other.


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