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Is quadrilateral ABCD a rectangle?

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by ahmedshafea » Mon Sep 11, 2017 12:45 pm
Is quadrilateral ABCD a rectangle?

(1) The diagonals (AC and BD) are perpendicular to each other
(2) The sum of any 3 angles in the quadrilateral is 270 degrees

What's the best way to determine whether statement 1 is sufficient?
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Source: — Data Sufficiency |

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by ErikaPrepScholar » Tue Sep 12, 2017 11:43 am
The easiest way to determine whether statement 1 is sufficient is to draw out possible options:

Image

Starting with two perpendicular diagonals that are the same length and intersect at their midpoints gives a square, which is a rectangle.

However, changing the length and midpoints of the lines gives:

Image

Which is not a rectangle.
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