Geometry QB - No. 7

by **HARISH** Tue Aug 28, 2007 2:19 pm

Is quadrilateral ABCD a rhombus?

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

(2) AB = BC = CD = AD

According to choice B (2), ABCD can also be a SQUARE. Am i right??

by **Harish Dorai** Tue Aug 28, 2007 2:51 pm

It can be a square only if the individual angles are 90 degrees. As per definition, SQUARE is actually a subset of RHOMBUS. So with the given information, we can certainly say that the quadrilateral is a Rhombus, but we cannot say it is a SQUARE.

by **Jimmy** Thu May 15, 2008 1:21 pm

Ron, Can you chime in with a better explanation than this? I am also confused...I would think B is not enough to tell us if it is a rhombus or square.

by **StaceyKoprince** Mon May 26, 2008 11:11 am

Harish is right. A rhombus is a quad that has all 4 sides the same (which also means that the opposite angles are equal). A square is a rhombus that ALSO has 90-degree angles for the four angles.

So (2) tells us the shape is a rhombus. It may or may not be a square - that would depend upon the angle measures, which we don't know.