Question

select all the statements that are true for all parallelograms.
all angles of a parallelogram are congruent.
all sides of a parallelogram are equal in length.
consecutive interior angles are supplementary.
the diagonals of a parallelogram are congruent.
the opposite sides of a parallelogram are congruent.

Explanation:

Step1: Analyze "All angles of a parallelogram are congruent."

In a general parallelogram (not a rectangle or square), adjacent angles are supplementary but not all angles are congruent (e.g., a rhombus with non - right angles). So this statement is false.

Step2: Analyze "All sides of a parallelogram are equal in length."

A general parallelogram has opposite sides equal. Only special parallelograms like rhombus have all sides equal. So this statement is false.

Step3: Analyze "Consecutive interior angles are supplementary."

In a parallelogram, since opposite sides are parallel, by the consecutive interior angles theorem (if two parallel lines are cut by a transversal, consecutive interior angles are supplementary), consecutive interior angles of a parallelogram are supplementary. This statement is true.

Step4: Analyze "The diagonals of a parallelogram are congruent."

In a general parallelogram (not a rectangle or square), the diagonals are not congruent. For example, in a rhombus (a type of parallelogram) with non - right angles, the diagonals have different lengths. So this statement is false.

Step5: Analyze "The opposite sides of a parallelogram are congruent."

This is a fundamental property of a parallelogram. By the definition and properties of parallelograms, the opposite sides are parallel and congruent. This statement is true.

Answer:

• Consecutive interior angles are supplementary.
• The opposite sides of a parallelogram are congruent.