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# ABCD is Quadrilateral and W, X, Y, Z are mid points of the

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ABCD is Quadrilateral and W, X, Y, Z are mid points of the [#permalink]  28 Apr 2012, 06:44
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ABCD is Quadrilateral and W, X, Y, Z are mid points of the side AB, BC, CD, DA respectively. what kind of Quadrilateral is WXYZ

B. Parallelogram
C. Rhombus.
D. Rectangle
E. Square
[Reveal] Spoiler: OA

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Re: ABCD is Quadrilateral and W, X, Y, Z are mid points of the [#permalink]  30 Apr 2012, 02:04
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kotela wrote:
ABCD is Quadrilateral and W, X, Y, Z are mid points of the side AB, BC, CD, DA respectively. what kind of Quadrilateral is WXYZ

B. Parallelogram
C. Rhombus.
D. Rectangle
E. Square

Look at the diagram below:
Attachment:

Quadrilateral.png [ 6.26 KiB | Viewed 768 times ]
WX is a midsegment of triangle ABC (a midsegment is a line segment joining the midpoints of two sides of a triangle). Now, the midsegment is always parallel to the third side of the triangle, so WX||AC. Similarly YZ is a midsegment of triangle CDA, hence YZ||AC. Therefore WX||YZ.

The same way we can get that XY||ZW.

So, we have that the opposite sides of quadrilateral WXYZ are parallel, which means that WXYZ is a parallelogram.

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Re: ABCD is Quadrilateral and W, X, Y, Z are mid points of the [#permalink]  03 May 2012, 21:35
Great Question
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Re: ABCD is Quadrilateral and W, X, Y, Z are mid points of the [#permalink]  04 May 2012, 16:48

Posted from GMAT ToolKit
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Re: ABCD is Quadrilateral and W, X, Y, Z are mid points of the [#permalink]  04 May 2012, 21:26
nmartelo wrote:

Posted from GMAT ToolKit

Though I agree that the GMAT won't give such options.
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Re: ABCD is Quadrilateral and W, X, Y, Z are mid points of the [#permalink]  04 May 2012, 21:40
thanks Bunuel, one more question, if the figure was a complex quadrilateral, the mid points also create a parallelogram?
Re: ABCD is Quadrilateral and W, X, Y, Z are mid points of the   [#permalink] 04 May 2012, 21:40
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# ABCD is Quadrilateral and W, X, Y, Z are mid points of the

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