Which of the following conditions are necessary and sufficient for a quadrilateral to be a square?
(1)All sides are of same length
(2) All angles are equal
(3) Diagonals are perpendicular to each other
(4) Diagonals are of same length
(5) Opposite sides should be parallel
Which of the following conditions are necessary and sufficient for a quadrilateral to be a square?
(1)All sides are of same length
(2) All angles are equal
(3) Diagonals are perpendicular to each other
(4) Diagonals are of same length
(5) Opposite sides should be parallel
The correct option is C 3 and 4
We can find exceptions for options (a), (b), (d) where by the conditions given we can construct a quadrilateral which is not square.
(a)All sides same length, diagonals perpendicular A Rhombus is also possible
(b)Angles equal, equal diagonals lengths A rectangle satisfies this condition.
(c)Diagonals perpendicular to each other and of same lengths.
Only a square can be constructed using this condition.
(d)Sides are equal and opposite sides are parallel.
A rhombus is possible with given condition.
3 and 4
We can find exceptions for options (a), (b), (d) where by the conditions given we can construct a quadrilateral which is not square.
(a)All sides same length, diagonals perpendicular A Rhombus is also possible
(b)Angles equal, equal diagonals lengths A rectangle satisfies this condition.
(c)Diagonals perpendicular to each other and of same lengths.
Only a square can be constructed using this condition.
(d)Sides are equal and opposite sides are parallel.
A rhombus is possible with given condition.
