Question

which statement is not always true about a parallelogram? the opposite angles are congruent. the opposite sides are congruent. the opposite sides are parallel. the diagonals are congruent.

Explanation:

1. Recall the properties of a parallelogram:

• By definition, a parallelogram has opposite sides parallel (so "The opposite sides are parallel" is always true).
• A theorem states that in a parallelogram, opposite sides are congruent (so "The opposite sides are congruent" is always true).
• Another theorem states that in a parallelogram, opposite angles are congruent (so "The opposite angles are congruent" is always true).
• For the diagonals: In a general parallelogram (like a rhombus or a non - rectangular parallelogram), the diagonals are not congruent. Only in special parallelograms like rectangles and squares (which are also parallelograms) are the diagonals congruent. So "The diagonals are congruent" is not always true for a parallelogram.

Answer:

The diagonals are congruent.