Question

which of the following is a property of all squares?
no sides are parallel.
opposite sides are not congruent.
opposite vertex angles are not congruent.
the diagonals bisect each other.

Explanation:

Step1: Analyze the property of sides

A square has two pairs of parallel sides. So, "No sides are parallel" is incorrect. Also, all sides of a square are congruent, which means opposite sides are congruent. So, "Opposite sides are not congruent" is wrong.

Step2: Analyze the property of angles

All angles in a square are right angles (\(90^{\circ}\)). Opposite vertex angles are congruent. So, "Opposite vertex angles are not congruent" is incorrect.

Step3: Analyze the property of diagonals

In a square, the diagonals bisect each other. Let the square have vertices \(A\), \(B\), \(C\), \(D\) and diagonals \(AC\) and \(BD\) intersecting at point \(O\). Using the properties of a square (all sides equal, all angles \(90^{\circ}\) and triangle congruence (e.g., \(\triangle ABC\cong\triangle ADC\) by SSS - Side - Side - Side congruence criterion if we consider the sides of the square and the diagonal as a common side)), we can show that \(AO = OC\) and \(BO=OD\). So, "The diagonals bisect each other" is a property of all squares.

Answer:

The diagonals bisect each other.