Advertisements
Advertisements
Question
Diagonals of a quadrilateral are perpendicular to each other. Is such a quadrilateral always a rhombus? Give a figure to justify your answer.
Advertisements
Solution
It is not necessary that a quadrilateral having perpendicular diagonals is a rhombus.
E.g. Consider a trapezium ABCD in which AB || CD.

APPEARS IN
RELATED QUESTIONS
The following figure is parallelogram. Find the degree values of the unknown x, y, z.

Diagonals of parallelogram ABCD intersect at O as shown in the following fegure. XY contains O, and X, Y are points on opposite sides of the parallelogram. Give reasons for each of the following:
(i) OB = OD
(ii) ∠OBY = ∠ODX
(iii) ∠BOY = ∠DOX
(iv) ∆BOY ≅ ∆DOX
Now, state if XY is bisected at O.

Points E and F lie on diagonal AC of a parallelogram ABCD such that AE = CF. What type of quadrilateral is BFDE?
Which of the following statement is true for a rhombus?
It is a quadrilateral.
The diagonals of a parallelogram are not perpendicular. Is it a rhombus? Why or why not?
If the diagonals of a rhombus are 12 cm and 16cm, find the length of each side.
Draw a rhombus, having each side of length 3.5 cm and one of the angles as 40°.
Measure of one angle of a rhombus is 50°, find the measures of remaining three angles.
In rhombus ABCD;
(i) if ∠A = 74° ; find ∠B and ∠C.
(ii) if AD = 7.5 cm ; find BC and CD.
The given figure shows a rhombus ABCD in which angle BCD = 80°. Find angles x and y.

