For a quadrilateral to be a square, the diagonals must be congruent and perpendicular.

A square has the following properties:

1. All sides are of equal length.
2. All angles are right angles (90°).
3. The diagonals are congruent (they have the same length).
4. The diagonals are perpendicular to each other (they intersect at right angles).
5. The diagonals bisect each other at right angles.

So, the correct answer is: congruent and perpendicular.

Would you like more details on the properties of squares or help with another geometry concept?

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Related questions:

1. What is the relationship between the diagonals in a rectangle?
2. How do the diagonals of a rhombus differ from those of a square?
3. How can you determine if a quadrilateral is a square given certain properties?
4. What is the difference between a square and a rectangle?
5. What other quadrilaterals have perpendicular diagonals?

Tip: When working with quadrilaterals, it's often helpful to remember the key properties of each type, such as congruency, perpendicularity, and parallelism, to identify or prove specific characteristics.