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Is quadrilateral ABCD a rectangle?

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by gmattesttaker2 » Sat Feb 15, 2014 8:12 pm
Hello,

Can you please assist with this:

Is quadrilateral ABCD a rectangle?

(1) The angles with vertices on A and B are right angles.

(2) AC = BD


The answer says C but I thought it must be E since both a square and a rectangle satisfy this condition as shown in "Statements_1_and_2.png"
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Quadrilateral ABCD
Statements_1_and_2.png
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by Patrick_GMATFix » Sat Feb 15, 2014 9:47 pm
Sri,

A square is a subset of the rectangle family, just as a rectangle is a type of quadrilateral (whose opposite sides are parallel), just as a quadrilateral is a type of polygon (which has 4 sides). A square is a special type of rectangle with equal sides.

As a result, if something is a square, it must be a rectangle

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Is quadrilateral ABCD a rectangle?

by Brent@GMATPrepNow » Sun Feb 16, 2014 9:39 am
Here's a diagram to add to what Patrick said:
Image

So, as you can see, a parallelogram is a type of quadrilateral (with 2 sets of parallel lines)
A rectangle and a rhombus are types of parallelograms.
A square is a type of rectangle
A square is a type of rhombus

So, for example, if ABCD is a square, then we can also call ABCD a rhombus, a rectangle, a parallelogram or a quadrilateral.

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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