Write ‘T’ for true and ‘F’ for false of 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.

(i) We can consider rhombus as a parallelogram.

And we know that diagonals of rhombus are not equal.

So we can conclude that diagonals of a parallelogram are not equal.

(ii) No, as a general rule the diagonals of a parallelogram do not bisect each other at right angles.

The definition of a parallelogram is a four-sided polygon with opposite sides parallel and equal in length. For the special case in which the 4 vertices of the parallelogram are right angles, we refer to the figure as a square, and for a square the diagonals do bisect each other at right angles.

For all parallelograms that are not squares, the diagonals do not intersect at right angles.

(iii)

ABCD is a rhombus . → AB = CD

Also diagonals bisects ach other → DO = OB

AO is common . So,

Triangle AOD is congruent to triangle AOB

So , Angle AOD = Angle AOB …… (C.P.C.T)

But , Angle AOD + Angle AOB = 180 …… (Linear pair)

So , Angle AOD = Angle AOB = 90
(iv) No, because a rhombus does not have to have 4 right angles. Kites have two pairs of adjacent sides that are equal