Question

select the correct answer. which of these sentences is always true for a parallelogram? a. all sides are congruent. b. all angles are congruent. c. the diagonals are congruent. d. opposite angles are congruent.

Explanation:

• Option A: In a parallelogram, only opposite sides are congruent. All sides are congruent only in special parallelograms like rhombus. So, this is not always true.
• Option B: In a parallelogram, only opposite angles are congruent. All angles are congruent only in special parallelograms like rectangle. So, this is not always true.
• Option C: The diagonals of a parallelogram bisect each other but are congruent only in special parallelograms like rectangle. So, this is not always true.
• Option D: By the properties of a parallelogram, opposite angles are always congruent.

Answer:

D. Opposite angles are congruent.