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Which of the ...
Question

Which of the following statements are correct?
Statement 1: There are 4 sides in a square.
Statement 2: A square is a quadrilateral.
Statement 3: A triangle is a quadrilateral.
Statement 4: A rectangle is a quadrilateral.

A
Statements 1, 2, and 4 are correct.
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B
Only statements 1 and 2 are correct.
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C
Only statements 1 and 3 are correct.
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D
Only statement 1 is correct.
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Solution

The correct option is A Statements 1, 2, and 4 are correct.
A quadrilateral is a closed 2D shape that has four sides.
A triangle has 3 sides. Hence, it is not a quadrilateral. Statement 3 is incorrect.
A square has 4 sides. Hence, it is a quadrilateral. Statements 1 and 2 are correct.
A rectangle has 4 sides. Hence, it is a quadrilateral. Statement 4 is correct.

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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.

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)

Q. Read the given statements and answer the following question.
(i) A triangle is a quadrilateral.
(ii) There are 4 sides in a quadrilateral.
(iii) A square is a quadrilateral.
How many of the above statements are correct?
Q. Determine if the given statements are sometimes , always or never true.
(i) A parallelogram is a quadrilateral.
(ii) A parallelogram is a trapezium.
(iii) A rhombus is a square.
(iv) A trapezium is a quadrilateral.
(v) A rectangle is a square.
Q. Given the true statement: If a quadrilateral is a square, then it is a rectangle. It follows that, of the converse and the inverse of this true statement.
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