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basic Geometry

by Azizakaria » Thu Jan 28, 2016 7:54 am
If a quadrilateral has four 90° angles and sides of length 3, 3, 8, and 8, it is which of
the following figures: square, rectangle, parallelogram, trapezoid?


The answer is :
It is a rectangle, parallelogram, and trapezoid, but it is not a square.

how parallelogram, and trapezoid can have a 90 angles ( without turning them to rectangle) ??
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by MartyMurray » Thu Jan 28, 2016 9:02 am
A parallelogram is defined as a four sided figure that has two sets of opposite sides that are parallel to each other. So rectangles and squares are special types of parallelograms.

There are two ways I have seen trapezoid defined. One way merely calls it a four sided figure with two parallel sides. The other way defines a trapezoid as a figure that has only two parallel sides.

So a rectangle is definitely a parallelogram, and if you were to go with the first definition of trapezoid, a rectangle could be a special form of a trapezoid, though if you were to go with the second definition, then a rectangle would not also not be a trapezoid.
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by Matt@VeritasPrep » Fri Jan 29, 2016 4:55 pm
The trapezoid controversy is the result of a dispute between elementary geometry teachers (who think of a trapezoid as having exactly one set of parallel sides) and the mathematicians (who think of a trapezoid as having AT LEAST one set of parallel sides).

IMO the second definition is the better one, as a lot of higher math will break down without it, but we're still at an math-cultural impasse. I don't think the GMAT will take a side in the debate, so you shouldn't see any questions requiring you to have an opinion on whether a square is a trapezoid.
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by Brent@GMATPrepNow » Fri Jan 29, 2016 8:39 pm
Here's how trapezoids are defined in the Official Guide:
A quadrilateral with two sides that are parallel is a trapezoid.

As Matt says, it's doubtful that the test-makers would ever construct a question that hinges on whether a trapezoid has exactly one pair of parallel lines or at least one pair of parallel lines.

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