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Standard VI

Mathematics

Quadrilateral

In a parallel...

Question

In a parallelogram, if the opposite sides are equal and every angle is a right angle, then the parallelogram is a ________.

trapezium

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kite

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rhombus

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rectangle

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Solution

The correct option is D rectangle
In a parallelogram, if the opposite sides are equal and every angle is a right angle, then the parallelogram is a rectangle.

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Similar questions

Q. Match the following.

(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.

Q. Match the following.

$(1)$ 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.

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)

Which of the following statements are true (T) and which are false (F) ?

(i) In a parallelogram, the diagonals are equal.

(ii) In a parallelogram, the diagonals bisect each other.

(iii) In a parallelogram, the diagonals bisect each other at right angles.

(iv) In any quadrilateral, if a pair of opposite sides is equal, it is a parallelogram.

(v) If all the angles of a quadrilateral are equal, it is a parallelogram.

(vi) If three sides of a quadrilateral are equal, it is a parallelogram.

(vii) If three angles of a quadrilateral are equal, it is a parallelogram

(viii) If all the sides of a quadrilateral are equal it is a parallelogram.

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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In a parallelogram, if the opposite sides are equal and every angle is a right angle, then the parallelogram is a ________.

The correct option is D rectangleIn a parallelogram, if the opposite sides are equal and every angle is a right angle, then the parallelogram is a rectangle.

The correct option is D rectangle
In a parallelogram, if the opposite sides are equal and every angle is a right angle, then the parallelogram is a rectangle.