Q3 of 58 Page 17

The diagonals of a parallelogram are not perpendicular. Is it a rhombus? Why or why not?

No, Diagonals of a rhombus bisect each other at 90°.


A parallelogram is rhombus only when its diagonals bisect each other at right angles.


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1

Which of the following statements are true for a rhombus?

(i) It has two pairs of parallel sides.


(ii) It has two pairs of equal sides.


(iii) It has only two pairs of equal sides.


(iv) Two of its angles are at right angles.


(v) Its diagonals bisect each other at right angles.


(vi) Its diagonals are equal and perpendicular.


(vii) It has all its sides of equal lengths.


(viii) It is a parallelogram.


(ix) It is a quadrilateral.


(x) It can be a square.


(xi) It is a square.

2

Fill in the blanks, in each of the following, so as to make the statement true:

(i) A rhombus is a parallelogram in which _______.


(ii) A square is a rhombus in which _________.


(iii) A rhombus has all its sides of ______ length.


(iv) The diagonals of a rhombus _____ each other at ______ angles.


(v) If the diagonals of a parallelogram bisect each other at right angles, then it is a ______.

 4

The diagonals of a quadrilateral are perpendicular to each other. Is such a quadrilateral always a rhombus? If your answer is ‘No’, draw a figure to justify your answer.

 5

ABCD is a rhombus. If ∠ACB = 40°, find ∠ADB.