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Quadrilateral - Rectangle

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by visjain » Wed Jun 10, 2009 8:27 pm
If Q is a quadrilateral, is Q a rectangle?

1) Opposite sides of Q are parallel.

2) One of the four angles of Q is 90 deg.

Please explain why this can't be a trapezoid with one angle at 90 deg and opposite sides being parallel.

OA [spoiler](C)[/spoiler]
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by tohellandback » Wed Jun 10, 2009 10:16 pm
C because:
just draw a quadrilateral with one angle 90 degrees. then draw the opposite parallel sides, it will be a rectangle.
The powers of two are bloody impolite!!
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Re: Quadrilateral - Rectangle

by mikeCoolBoy » Wed Jun 10, 2009 11:10 pm
visjain wrote:If Q is a quadrilateral, is Q a rectangle?

1) Opposite sides of Q are parallel.

2) One of the four angles of Q is 90 deg.

Please explain why this can't be a trapezoid with one angle at 90 deg and opposite sides being parallel.

OA [spoiler](C)[/spoiler]
I think you should frame the question the other way around. Can I draw a trapezoid with one angle at 90 deg and with opposite sides parallel?
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Re: Quadrilateral - Rectangle

by Stuart@KaplanGMAT » Thu Jun 11, 2009 10:40 am
visjain wrote:If Q is a quadrilateral, is Q a rectangle?

1) Opposite sides of Q are parallel.

2) One of the four angles of Q is 90 deg.

Please explain why this can't be a trapezoid with one angle at 90 deg and opposite sides being parallel.
The problem might be with your interpretation of (1).

If you misinterpret (1) as "the quadrilateral has a pair of parallel sides", the shape doesn't have to be a rectangle.

However, the proper interpretation of (1) is that all the opposite sides of the shape are parallel, i.e. it has two pairs of parallel sides. Under this interpretation, if one angle is 90 degrees all of the angles have to be 90 degrees and the shape is, in fact, a rectangle.
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