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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 A. Quadrilateral B. Parallelogram C. Rhombus. D. Rectangle E. Square
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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
A. Quadrilateral
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. Answer: B.
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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
What about a? Aren't they all quadrilaterals?  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
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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?
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Re: ABCD is Quadrilateral and W, X, Y, Z are mid points of the
[#permalink]
04 May 2012, 21:40
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