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# Is ABCD a rectangle? (1) ∠ADC = 90° (2) AD = BC

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Bunuel wrote:

Is ABCD a rectangle?

Attachment:
The attachment GMAT_DS_Magoosh_157.png is no longer available

We need to determine whether all the four angles of the quadrilateral ABCD are 90 degree or not. Because a rectangle has all the four angles 90 (side lengths don't matter). When all the sides are equal then it is a square, otherwise it's a rectangle and every square is a rectangle.

St1:- ∠ADC = 90°. We don't know the measure of other three angles ,those sum to 360-90=270.
When they are equal, then each measures 90 degree and the quadrilateral becomes a rectangle. Otherwise, it's just a quadrilateral but not rectangle.
Insufficient.
Side doesn't help in determining type of quadrilateral specifically. Insufficient.

Combining, we have the same situation as mentioned in (1). We can draw rectangles with AD=BC and ∠ADC = 90°. And in the other case,it's not a rectangle.(See enclosed figure)
Insufficient.

Ans. (E)
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rectangle.JPG [ 23.91 KiB | Viewed 4073 times ]

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