Diamond ABCD

∴OA=OC= 1/2AC

OB=OD= 1/2BD

AC = BD

∴OA=OB

∵OA⊥OB (diagonal lines of diamonds are perpendicular to each other)

∴∠OAB=∠OBA=45

Similarly ∠ OBC = ∠ OCB = 45.

∴∠OBA+∠OBC=90

∴∠ABC=90

∴ABCD is square.

Analysis: ABCD is known to be a diamond, so it can be judged according to whether a diamond with a right angle is a square.

The test site of this question: positive judgment.

Test center comments: This question is the way to judge a square. According to the concept of square, there are two ways to judge whether a quadrilateral is a square:

First it is a rectangle, and then a group of adjacent sides are equal;

(2) First it is a diamond, then it has a right angle.