#### description

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

#### notes

A square is a rectangle with equal sides. This means a square has all the properties of a rectangle with an additional requirement that all the sides have equal length.

In a square the diagonals.

(i) bisect one another (square being a parallelogram)

(ii) are of equal length (square being a rectangle) and

(iii) are perpendicular to one another.

**Property:** The diagonals of a square are perpendicular bisectors of each other.

ABCD is a square whose diagonals meet at O .

OA = OC (Since the square is a parallelogram)

By SSS congruency condition, we now see that

∆ AOD ≅ ∆ COD

Therefore, m∠AOD = m∠COD

These angles being a linear pair, each is right angle.

#### Shaalaa.com | Property: The diagonals of a square are perpendicular bisectors of each other.

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