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Implication

Combine these...

Question

Combine these two statements using, 'if and only if'

p:If a rectangle is a square, then all its four sides are equal.

q:If all the four sides of a rectangle are equal, then the rectangle is a square.

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Solution

A rectangle is a square, if and only if all its four sides are equal.

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Similar questions

Q. Complete each of the following statements by means of one of those given in brackets against each:
(i) If one pair of opposite sides are equal and parallel, then the figure is ........................
(parallelogram, rectangle, trapezium)

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

(iii) A line 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) Consecutive angles of a parallelogram are ...................
(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)

Q. If all sides of a rectangle are equal, then it becomes a _______ .

Q. Fill in the blanks.
(i) A polygon having all sides equal and all angles equal is called a ...... polygon.
(ii) Perimeter of a square = ...... × side.
(iii) Area of a rectangle = (......) × (......).
(iv) Area of a square = ...... .
(v) If the length of a rectangle is 5 m and its breadth is 4 m, then its area is ...... .

Q. Use deductive logic and conclude for the following statements-
All squares are rectangles.
All rectangles have four sides.

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)

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