How sure that it is rhombus

[pardeepnbp]

Is quadrilateral ABCD a rhombus?

(1) Line segments AC and BD are perpendicular bisectors of each other.

(2) AB = BC = CD = AD


Answer is D, each statement is sufficient.

I agree with stat 1 but not 2..
Analyzing Statement 2 independently tells us that quadrilateral ABCD can be square or rhombus because both have the equal sides only varying in angles.

I need the expert comments

[lokeshvgopal]

u can for sure tell that if all sides of a quadrilateral are equal, then the polygon is a rhombus... but to tell its a square u need more info - say, angles are all 90 .

hence option D is correct for the case.

[cyber_office]

Hi,

According to 1, the diagonals are perpendicular to each other. This means it could be a square or a rhombus.

According to 2, all sides are equal. This means it could be a square or a rhombus.

However, we know that the rhombus is a special case of an equilateral quadrilateral and that a square is special case of a rhombus. Hence, rhombus = square (with exception of 90 degree angles), which means that each statement by itself is sufficient to conclude that the figure is a rhombus.

CY

[Ben Ku]

This question has been addressed several times. Here's one:[url]
post3521.html?hilit=quadrilateral%20ABCD%20rhombus#p3521[/url]