ABCD Rhombus

by **pahwa.suneet** Fri Mar 25, 2011 9:57 am

Hi Guys,
I have a problem in below question from MGMAT Geometry question bank:
Is quadrilateral ABCD a rhombus?

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

(2) AB = BC = CD = AD

My problem is that statement (2) can also mean it is a square. But, the answer soln. states that each statement alone is sufficient.

Sincerely,
SP

by **david.khoy** Mon Mar 28, 2011 3:46 am

A square is a rhombus with a right angle.

Statement 2 is sufficient, because a rhombus is a quadrilateral whose four sides all have the same length, regardless of the angles values.

by **jnelson0612** Fri Apr 01, 2011 1:08 pm

Thank you David.

by **mengnu.liang** Sat Apr 14, 2012 12:26 pm

jnelson0612 Wrote:Thank you David.

Wait I thought ALL sides of Rhombus have to be equal. Statement 1 doesn't specify that. Shouldn't the answer be C?

by **tim** Wed Apr 25, 2012 5:38 pm

statement 1 doesn't specify that, but if you draw any quadrilateral with diagonals that are perpendicular bisectors it will be a rhombus. remember in geometry problems you need to take what you are given and derive all implications from it. in this case, the implication is that we have a rhombus..

ABCD Rhombus

ABCD Rhombus

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Re: ABCD Rhombus

Re: ABCD Rhombus

Re: ABCD Rhombus