Konstantin Lynov wrote:
Is ABCD a rectangle?
1) AC(imagine: diagonal of a quadrilateral) bisect BD (imagine: another diagonal of a quadrilateral) bisect each other in point E
2) Angle ABC = 90 degrees
As I see opinions differ.
The key here lies in the word bisect
, which is to divide in halfs.
From the first statement the figure could be a rombus and a rectangle. Insufficient.
From the second statement it could be anything with a 90 degree angle. Imagine an ugly figure with two relatively short sides and a 90 degree angle between them and with third and forth sides realy-realy long ones, ending up in the stratosphere. Insufficient.
Combining the statement is sufficient.