To determine which of the following is not a property of all parallelograms, let's review the fundamental properties of parallelograms. A parallelogram is a quadrilateral with both pairs of opposite sides parallel. Here are the standard properties:
1. Opposite sides are congruent: This means each pair of opposite sides has the same length. This is a fundamental property of parallelograms.
2. Diagonals are congruent: This is not a universal property of all parallelograms. While in some specific types of parallelograms, such as rectangles, diagonals are congruent, it does not hold true for all parallelograms. For example, in a general parallelogram (without right angles), the diagonals typically differ in length.
3. Opposite angles are congruent: This means each pair of opposite angles has the same measure. This is a defining property of parallelograms.
4. Opposite sides are parallel: This is the very definition of a parallelogram, as both pairs of opposite sides must be parallel.
Considering the properties listed above, the one that is not characteristic of all parallelograms is:
(2) Diagonals are congruent
Thus, option (2) is the correct answer.
