Which of the following is/are correct?

(i) All rhombuses are parallelograms.
(ii) All squares are rhombuses and also rectangles.
(iii) All rectangles are squares.

A. Only (i) B. Only (ii) C. (i) & (ii) D. (ii) & (iii)

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Solution

(i) The necessary condition for a quadrilateral to be a parallelogram is the opposite sides should be parallel and equal, which is true for a rhombus. So, all rhombuses are parallelograms.

(ii) The necessary condition for a quadrilateral to be a rhombus is opposite sides are parallel and all sides are equal. Whereas for a rectangle, opposite sides are equal, and all interior angles are equal to 90°. These conditions are met by all squares, so all squares are rhombuses and also rectangles.

(iii) The necessary condition for a quadrilateral to be a square is all sides are equal and all interior angles are equal to 90°.
As it is not necessary for a rectangle that all its sides are equal, not every rectangle is a square.

So, (i) and (ii) are only true.

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Similar questions

State with reasons whether the following statements are ‘true’ or ‘false’.

(i) Every parallelogram is a rhombus.

(ii) Every rhombus is a rectangle.

(iii) Every rectangle is a parallelogram.

(iv) Every squre is a rectangle.

(v) Every square is a rhombus.

(vi) Every parallelogram is a rectangle.

State whether true or false.

(a) All rectangles are squares.
(b) All rhombuses are parallelograms.
(c) All squares are rhombuses and also rectangles.
(d) All squares are not parallelograms.

Find which of the following are true:

1.All rhombuses are squares
2.All squares are rectangles
3.All rectangles are parallelograms
4.All parallelograms are quadrilaterals
5.All parallelograms are rhombuses

Q. Answer the tick ones
1. Which of the following statements are true for a rectangle?
(i) It has two pairs of equal sides.
(ii)It has all its sides of equal length.
(iii) Its diagonal are equals.
(iv) Its diagonals bisect each other.
(v) Its diagonals are perpendicular.
(vi) Its diagonals are perpendicular and bisect each other.
(vii) Its diagonals are equal and bisect each other.
(viii)lts diagonals are equal and perpendicular, and bisect each other .
(ix) All rectangles are Squares.
(x) All rhombuses are parallelograms.
(xi)All squares are rhombuses and also rectangles.
(xii) All squares are not parallelograms.
2. Which of the following statements are true for a square?
(i) It is a rectangle.
(ii) It has all its sides of equal length.

Which of the following are true?

i) All squares are rhombuses.

ii) All parallelograms are rectangles.

iii) All rhombuses are trapeziums

iv) All squares are rectangles.

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Which of the following is/are correct? (i) All rhombuses are parallelograms. (ii) All squares are rhombuses and also rectangles. (iii) All rectangles are squares. A. Only (i) B. Only (ii) C. (i) & (ii) D. (ii) & (iii)

Which of the following is/are correct?

(i) All rhombuses are parallelograms.
(ii) All squares are rhombuses and also rectangles.
(iii) All rectangles are squares.

A. Only (i) B. Only (ii) C. (i) & (ii) D. (ii) & (iii)