# Properties of a Square - Property: The diagonals of a square are perpendicular bisectors of each other.

## Theorem

### The diagonals of a square are perpendicular bisectors of each other.

Given: ABCD is a square, where AC and BD is a diagonal bisect each other at a Point 'O'.

To Prove: ∠AOD = ∠COD = 90°.

Proof:

ABCD is a square whose diagonals meet at O. ......(Given)

OA = OC.                                                          ......(Since the square is a parallelogram)(1)

In ΔAOD and ∆COD,
OD = OD           .........(Common side)
OA = OC            .........(From 1)
AD = DC            ..........(All the sides of square have equal length.)

By SSS congruency condition,
∆AOD ≅ ∆COD

Therefore, m∠ AOD = m∠ COD  ......(C.A.C.T.)

Since, m∠ AOD and m∠ COD are a linear pair,

∠AOD = ∠COD = 90°.

Hence Proved.

If you would like to contribute notes or other learning material, please submit them using the button below.

### Shaalaa.com

The diagonals of a square are perpendicular bisectors of each other. [00:12:42]
S
0%