Question

How did we prove that these vertices form a square? (select all that apply)showed that the diagonals are congruentshowed that the diagonals are perpendicularproved that the vertices formed a parallelogramshowed that the diagonals bisected each otherproved that the sides were congruentshowed that the sides of the quadrilateral are perpendicular

Answer 1

To prove that a quadrilateral formed by four vertices is a square, the following conditions can be verified:

1. **Showed that the diagonals are congruent**: In a square, the diagonals are of equal length.

2. **Showed that the diagonals are perpendicular**: In a square, the diagonals intersect at right angles (90 degrees).

3. **Proved that the vertices formed a parallelogram**: A square is a specific type of parallelogram, which means that this property holds true.

4. **Showed that the diagonals bisected each other**: In a parallelogram, the diagonals bisect each other, and this is also true for squares.

5. **Proved that the sides were congruent**: All sides of a square are equal in length.

6. **Showed that the sides of the quadrilateral are perpendicular**: In a square, each side is perpendicular to its adjacent sides.

To conclude, all the options you provided can be used as part of the proof that the vertices form a square. Thus, you should select all of the options listed.