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Some Special Parallelograms - Concept of a Square

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  • 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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