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Geometry -- quadrilaterals

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guest
 Post subject: Geometry -- quadrilaterals
 Post Posted: 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.
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columbus13
 Post subject: a square is a special case of a rectange
 Post Posted: 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
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Raj
 Post subject: Geometry -- quadrilaterals
 Post Posted: Mon Jul 14, 2008 5:24 pm 
By Definition, All SQUARES are RECTANGLES, hence C is right.
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rfernandez
 Post subject:
 Post Posted: Sat Jul 26, 2008 3:43 am 
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ManhattanGMAT Staff


Posts: 386
Agreed! Every square is a rectangle, hence C.
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skhalid
 Post subject: Re: Geometry -- quadrilaterals
 Post Posted: Wed Apr 22, 2009 11:39 pm 
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Posts: 4
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?
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RonPurewal
 Post subject: Re: Geometry -- quadrilaterals
 Post Posted: Sun May 03, 2009 4:39 am 
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ManhattanGMAT Staff


Posts: 7146
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.
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skhalid
 Post subject: Re: Geometry -- quadrilaterals
 Post Posted: Fri May 08, 2009 2:44 pm 
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Posts: 4
That makes sense. thanks!
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JonathanSchneider
 Post subject: Re: Geometry -- quadrilaterals
 Post Posted: Fri May 08, 2009 10:46 pm 
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ManhattanGMAT Staff


Posts: 480
Location: Durham, NC
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