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Parallelogram

Explain how a...

Question

Explain how a square is:

(i) A parallelogram
(ii) A rhombus

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Solution

(i) A parallelogram is a quadrilateral whose both pairs of opposite sides are equal and parallel, both pairs of opposite angles are equal and diagonals bisect each other.
Since, a square satisfies all the properties of a parallelogram, a square is also a parallelogram.

(ii) A square is a rhombus because it has four equal sides and diagonals bisect at $90^{\circ}$ to each other.

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Prove that :

(i) the parallelogram, inscribed in a circle, is a rectangle.

(ii) the rhombus, inscribed in a circle, is a square.

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.

Q. Which of the following statements are true and which are false?
(i) The diagonals of a parallelogram are equal.
(ii) The diagonals of a rectangle are perpendicular to each other.
(iii) The diagonals of a rhombus are equal.
(iv) Every rhombus is a kite.
(v) Every rectangle is a square.
(vi) Every square is a a parallelogram.
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(viii) Every rectangle is a parallelogram.
(ix) Every parallelogram is a rectangle.
(x) Every rhombus is a parallelogram.

Explain how a square is:

(i) A parallelogram
(ii) A rhombus

Q. Explain how a square is a-
(i) quadrilateral (ii) parallelogram (iii) rhombus (iv) rectangle.

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