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.