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Observing Quadrilaterals in Intersecting Circles

Which propert...

Question

Which property of the rhombus is used in its construction if the length of two diagonals are given?

A

All sides of a rhombus are equal.

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B

In a rhombus, diagonals bisect each other at right angles.

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C

Opposite angles of a rhombus are equal.

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D

Diagonals bisect the angles of a rhombus.

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Solution

The correct options are
B In a rhombus, diagonals bisect each other at right angles.
D Diagonals bisect the angles of a rhombus.
The diagonals of a rhombus are perpendicular bisectors of each other.
Now, if we join the end points of the diagonals, we can get the required rhombus.

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Similar questions

Q. Which of the following quadrilateral is not a rhombus?

(a) All four sides are equal

(b) Diagonals bisect each other

(c) Diagonals bisect opposite angles

(d) One angle between the diagonals is 60°

Q. Which of the quadrilaterals mentioned in brackets have the following properties?

(1) Diagonals are congruent. (square, rectangle, rhombus)
(2) The longer diagonal is the perpendicular bisector of the shorter and the shorter of the longer. (trapezium, kite, rhombus)
(3) All sides and angles are congruent. (rhombus, square, rectangle)
(4) Opposite angles are congruent. (kite, parallelogram, rectangle)
(5) Opposite sides are congruent. (trapezium, rectangle, parallelogram)
(6) Diagonals bisect each other at right angles. (square, rectangle, rhombus)
(7) Diagonals bisect each another. (rectangle, parallelogram, kite)
(8) One pair of opposite sides is parallel. (kite rhombus trapezium)

Q. 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 ......

Q. Write 'T' for true and 'F' for false for each of the following:
(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 bisect each other at right angles.
(iv) Every rhombus is a kite.

To construct rhombus ABCD given CD =5 cm and diagonal BD =8.5 cm, which of the properties of rhombus do we use?

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