Diagonals of Square at Algebra Den

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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.