State true or false:

If the diagonals of a quadrilateral are perpendicular to each other, then such a quadrilateral is always a rhombus.

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

True

False

answer is B.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Here, we have to decide that if the diagonals of a quadrilateral are equal, then it is always a rhombus or not. Accordingly, we have to state if the given statement is true or not.
Now, of all the known quadrilaterals, the ones whose diagonals are perpendicular are a rhombus and a square.
Next, it can be observed that there is no other information about the quadrilateral, like the side or angle measures, the diagonals are bisecting or not, etc.
Therefore, only on the basis of the condition that the diagonals are perpendicular, we cannot confidently say that the quadrilateral is a rhombus, as there is the possibility that it is a square as its diagonals are also perpendicular to each other according to its property.
Hence, the given statement is false.
Hence, the correct option is (2).

Watch 3-min video & get full concept clarity