Parallelogram Properties 0D18Fc

1. **State the problem:** We need to determine which statements are always true for a parallelogram. 2. **Recall properties of a parallelogram:** - Opposite sides are equal and parallel. - Opposite angles are equal. - Consecutive angles are supplementary. - The diagonals bisect each other (each diagonal cuts the other into two equal parts). - The diagonals do not necessarily bisect at right angles unless the parallelogram is a rhombus. 3. **Evaluate each statement:** - "Two pairs of adjacent sides are equal." This is false for a general parallelogram. Adjacent sides can be different lengths. This is true only for a rhombus or square. - "All angles are right angles." This is false for a general parallelogram. Only rectangles and squares have all right angles. - "The diagonals bisect each other at right angles." This is false for a general parallelogram. Only rhombuses and squares have diagonals that bisect at right angles. - "Exactly one diagonal bisects the other diagonal." This is false. In a parallelogram, both diagonals bisect each other. - "None of these." Since none of the above statements are always true for all parallelograms, this is true. 4. **Final conclusion:** The only statement always true for a parallelogram from the given options is "None of these."