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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.