Geometry -- quadrilaterals

by **guest** Thu Jul 10, 2008 4:16 pm

Is quadrilateral ABCD a rectangle?
(1) Line segments AC and BD bisect one another.

(2) Angle ABC is a right angle.

This question is from the MGMAT Geometry question bank. The official answer is C. But I think it should be E. The quadrilateral could be either a rectangle or square. Is this not correct?

Thanks for your help.

by **columbus13** Fri Jul 11, 2008 10:27 am

Since square is a special case of a rectange with 4 equal sides, i think c is the right answer

by **Raj** Mon Jul 14, 2008 5:24 pm

By Definition, All SQUARES are RECTANGLES, hence C is right.

by **rfernandez** Sat Jul 26, 2008 3:43 am

Agreed! Every square is a rectangle, hence C.

by **skhalid** Wed Apr 22, 2009 11:39 pm

I am struggling with this question.

A trapezoid can also satisfy both of these statements - AC and BD i.e. diagonals can intersect, and ABC can be a right angle. Isn't that correct?

by **RonPurewal** Sun May 03, 2009 4:39 am

skhalid Wrote:I am struggling with this question.

A trapezoid can also satisfy both of these statements - AC and BD i.e. diagonals can intersect, and ABC can be a right angle. Isn't that correct?

it doesn't just say that the diagonals intersect. it says that they bisect each other.
that means that each diagonal cuts the other diagonal exactly in half.

trapezoids can't do that; in fact, if the diagonals mutually bisect each other, this guarantees a parallelogram.

--

if you don't see this, try drawing the diagonals first:
* draw a bunch of pairs of segments, both of which bisect each other.
* use the endpoints of the segments as corners, and complete the resulting quadrilaterals.
* note that ALL of them are parallelograms.

by **skhalid** Fri May 08, 2009 2:44 pm

That makes sense. thanks!

by **JonathanSchneider** Fri May 08, 2009 10:46 pm