Question

which statement is true about all parallelograms? a all four sides are congruent. b the interior angles are all congruent. c two pairs of opposite sides are congruent. d the diagonals are perpendicular to each other.

Explanation:

Step1: Analyze option A

In a general parallelogram, all four sides are not congruent. Only in special parallelograms like rhombus (a type of parallelogram) all sides are congruent. So option A is false.

Step2: Analyze option B

In a general parallelogram, the interior angles are not all congruent. In a parallelogram, opposite angles are congruent. Only in a rectangle (a type of parallelogram) all angles are \(90^{\circ}\). So option B is false.

Step3: Analyze option C

By the property of parallelograms, two pairs of opposite sides are congruent. This is a fundamental property of parallelograms.

Step4: Analyze option D

In a general parallelogram, the diagonals are not perpendicular to each other. Only in a rhombus (a type of parallelogram) the diagonals are perpendicular. So option D is false.

Answer:

C. Two pairs of opposite sides are congruent.