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ABCD is Quadrilateral and W, X, Y, Z are mid points of the 28 Apr 2012, 06:44
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65% (hard)

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41% (01:12) correct 59% (01:04) wrong based on 29 sessions

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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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B
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Bunuel
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ABCD is Quadrilateral and W, X, Y, Z are mid points of the 30 Apr 2012, 02:04
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kotela
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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Look at the diagram below:
Attachment:
Quadrilateral.png
Quadrilateral.png [ 6.26 KiB | Viewed 10911 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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ABCD is Quadrilateral and W, X, Y, Z are mid points of the 03 May 2012, 21:35
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Great Question 8-)
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ABCD is Quadrilateral and W, X, Y, Z are mid points of the 04 May 2012, 16:48
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What about a? Aren't they all quadrilaterals?

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ABCD is Quadrilateral and W, X, Y, Z are mid points of the 04 May 2012, 21:26
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nmartelo
What about a? Aren't they all quadrilaterals?

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Yes, WXYZ is obviously a quadrilateral but the question asks what kind of quadrilateral is it.

Though I agree that the GMAT won't give such options.
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ABCD is Quadrilateral and W, X, Y, Z are mid points of the 04 May 2012, 21:40
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thanks Bunuel, one more question, if the figure was a complex quadrilateral, the mid points also create a parallelogram?
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ABCD is Quadrilateral and W, X, Y, Z are mid points of the 25 Sep 2014, 13:52
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