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...
DS- Parallegram, Kites, rhombus, quads etc Q1
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Kite - A quadrilateral with two disjoint pairs of congruent adjacent sides.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...
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.
Statement 1: This implies ABCD is a parallelogram --> Not sufficientkaps786 wrote:Is quadrilateral ABCD a rectangle?
(1) Line segments AC and BD bisect one another.
(2) Angle ABC is a right angle.
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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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.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.
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.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...?
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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