Is quadrilateral ABCD a rectangle?

[ahmedshafea]

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?

[ErikaPrepScholar]

The easiest way to determine whether statement 1 is sufficient is to draw out possible options:



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:



Which is not a rectangle.