The problem asks to "select the properties of all squares." Let's review each statement you selected to determine which ones are correct for a square:

1. Exactly one diagonal is bisected by the other diagonal: This is incorrect. In a square, both diagonals bisect each other.

2. The diagonals are perpendicular: This is correct. In a square, the diagonals meet at a 90-degree angle.

3. Opposite angles are congruent: This is correct. All angles in a square are 90 degrees, and opposite angles are congruent.

4. All sides are congruent: This is correct. A defining property of a square is that all sides are equal in length.

5. Opposite sides are congruent: This is correct. As all sides are equal, opposite sides are congruent.

6. All angles are congruent: This is correct. In a square, all four angles are 90 degrees.

7. The diagonals are congruent: This is correct. The diagonals in a square are equal in length.

8. Opposite sides are parallel: This is correct. Opposite sides of a square are parallel to each other.

9. The diagonals bisect each other: This is correct. In a square, the diagonals bisect each other at a 90-degree angle.

Corrected Properties:

• The following options should be selected for all squares:
  • The diagonals are perpendicular.
  • Opposite angles are congruent.
  • All sides are congruent.
  • Opposite sides are congruent.
  • All angles are congruent.
  • The diagonals are congruent.
  • Opposite sides are parallel.
  • The diagonals bisect each other.

Would you like further details or explanations on any of these properties?

Here are 5 related questions to consider:

1. What is the difference between a square and a rectangle in terms of diagonals?
2. How do the properties of a square compare to those of a rhombus?
3. Are the diagonals of a square always equal to its side lengths?
4. What is the relationship between the diagonals and area of a square?
5. How does the concept of symmetry apply to squares?

Tip: A square can also be considered a rectangle, rhombus, and parallelogram, because it satisfies the properties of each of these quadrilaterals.