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A a square

by sanju09 » Wed Apr 06, 2011 12:42 am
Is Figure A a square?

(1) Figure A is a parallelogram.

(2) All four sides of Figure A are 3 inches long and Figure A has at least one right angle.



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by GMATGuruNY » Wed Apr 06, 2011 2:10 am
sanju09 wrote:Is Figure A a square?

(1) Figure A is a parallelogram.

(2) All four sides of Figure A are 3 inches long and Figure A has at least one right angle.



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Statement 1: Figure A is a parallelogram.
Opposite sides are parallel.
Figure A could be a square.
Figure A could be a rhombus.
Insufficient.

Statement 2: All four sides of Figure A are 3 inches long and Figure A has at least one right angle.
By definition, a quadrilateral with 4 equal sides and at least 1 right angle is a square.
Sufficient.

The correct answer is B.

Here's a proof for Statement 2:
Let's call the figure ABCD.
Since all 4 sides are equal, ABCD is a square or a rhombus.
In both a square and a rhombus, opposite angles are equal.
Thus, if angle A = 90, then angle C = 90.
Since the sum of all 4 angles is 360, B+D = 360-90-90 = 180.
Since B and D must be equal, B=D=90.
Thus, all four angles are 90 degrees, all four sides are equal, and ABCD is a square.
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