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DS- Parallegram, Kites, rhombus, quads etc Q1

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by kaps786 » Thu Aug 18, 2011 6:10 am
Q-I) Is quadrilateral ABCD a rectangle?

(1) Line segments AC and BD bisect one another.

(2) Angle ABC is a right angle.


OA follows.....





OA C


My question is what properties and differences between these figures - squares, rhombus, kites, rectangles, etc we should remember are different & common...i.e key concepts on which the GMAT can test...

And does the GMAT really test kite properties...?

Posting a few more of these types to get a better flavour of these issues...

Thanks...
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by Anurag@Gurome » Thu Aug 18, 2011 7:42 am
kaps786 wrote:My question is what properties and differences between these figures - squares, rhombus, kites, rectangles, etc we should remember are different & common...i.e key concepts on which the GMAT can test...
Kite - A quadrilateral with two disjoint pairs of congruent adjacent sides.
Parallelogram - A quadrilateral with two pairs of parallel sides.
Rectangle - A parallelogram with four angles of equal size (right angles).
Rhombus - A parallelogram with four sides of equal length.
Square - A parallelogram with four sides of equal length and four angles of equal size (right angles).

Now the above statements are a variant of many available definitions of these shapes. This definitions also implies other properties of the shapes. For example, the diagonals of a parallelograms always bisect each other.

kaps786 wrote:Is quadrilateral ABCD a rectangle?

(1) Line segments AC and BD bisect one another.
(2) Angle ABC is a right angle.
Statement 1: This implies ABCD is a parallelogram --> Not sufficient

Statement 2: Only one right angle does not ensure that ABCD is a rectangle --> Not sufficient

1 & 2 Together: ABCD is a parallelogram with one right angle. This implies other three angles of ABCD are also right angles. Hence, ABCD is a rectangle --> Sufficient

The correct answer is C.
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by ccma86 » Tue Aug 28, 2012 12:22 pm
I understand that the shape is a parallelogram and that each of its four angles are right triangles. But, couldn't this also be a square? Why or why not? Thanks.
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by Ian Stewart » Tue Aug 28, 2012 5:26 pm
ccma86 wrote:I understand that the shape is a parallelogram and that each of its four angles are right triangles. But, couldn't this also be a square? Why or why not? Thanks.
The word rectangle comes from the latin 'rectus' meaning 'right', so a rectangle is just any quadrilateral with four right angles. That includes squares - squares are a special type of rectangle in which all the sides are of equal length. So yes, the shape could be a square, but then it is also a rectangle.
kaps786 wrote:
My question is what properties and differences between these figures - squares, rhombus, kites, rectangles, etc we should remember are different & common...i.e key concepts on which the GMAT can test...

And does the GMAT really test kite properties...?
I have never seen the word 'rhombus' or 'kite' in a real GMAT question, and I've seen several thousand of the things, so I would be very, very surprised if you saw either of those words on test day. Of course you could see a shape in a diagram which happens to be a kite, say, but you'd always be able to work out from the diagram the answer to the question without needing to have memorized any special properties of kites.

You should certainly understand squares, rectangles and parallelograms, however - how to find their areas, and the simple facts about their angles (specifically, in a parallelogram, opposite angles are equal and adjacent angles add to 180).
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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