Nadeem has created a flowchart to specify whether a given quadrilateral is a square or not. If the answer is yes (for the input question), it is considered as a square, and if it is no, it is not considered as a square. Which of these is the best question to ask to find out whether the quadrilateral is a square or not?
a) "Are all the angles in the square right angles?" (A rectangle also has all angles=90^o)
b) "Are the opposite sides equal?" (opp. sides equal for square, parallelogram, rectangle, rhombus)
c) "Are any two adjacent sides of the figure equal?" (equal for rhombus, square, also for kite, but not any two adjacent sides)
d) "Are the opposite angles of the figure equal?" (equal for square, rectangle, parallelogram, rhombus)

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Solution

Out of the four questions, answers of the following two questions are necessary and sufficient to check whether the quadrilateral is square or not.
The questions are as follows-
c) "Are any two adjacent sides of the figure equal?"
d) "Are the opposite angles of the figure equal?"

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Similar questions

Complete each of the following statements by means of one of those given in brackets against each :

(i) If one pair of opposite sides is equal and parallel, then the figure is ........

(parallelogram, rectangle, trapezium)

(ii) If in a quadrilateral only one pair of opposite sides is parallel, the quadrilateral is .......

(square, rectangle, trapezium)

(iii) A line is drawn from the mid-point of one side of a triangle ......, another side intersects the third side at its mid-point.

(perpendicular to, parallel to, to meet)

(iv) If one angle of a parallelogram is a right angle, then it is necessarily a ......

(rectangle, square, rhombus)

(v) The consecutive angle of a parallelogram is......

(supplementary, complementary)

(vi) If both pairs of opposite sides of a quadrilateral are equal, then it is necessarily a ........

(rectangle, parallelogram, rhombus)

(vii) If opposite angles of a quadrilateral are equal, then it is necessarily a ...........

(parallelogram, rhombus, rectangle)

(viii) If consecutive sides of a parallelogram are equal, then it is necessarily a ..........

(kite, rhombus, square)

(1)	Rectangle	(p)	A quadrilateral having its opposite sides equal and parallel.
(2)	Square	(q)	A parallelogram having its opposite sides equal and each of the angle is a right angle.
(3)	Parallelogram	(r)	A parallelogram having all sides equal and each of the angle is a right angle.
(4)	Rhombus	(s)	A quadrilateral in which a pair of opposite sides are parallel.
(5)	Trapezium	(t)	A parallelogram having all sides equal.

$(1)$ Rectangle	(p) A quadrilateral having its opposite sides equal and parallel.
$(2)$ Square	(q) A parallelogram having its opposite sides equal and each of the angle is a right angle.
$(3)$ Parallelogram	(r) A parallelogram having all sides equal and each of the angle is a right angle.
$(4)$ Rhombus	(s) A quadrilateral in which a pair of opposite sides are parallel.
$(5)$ Trapezium	(t) A parallelogram having all sides equal.

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