Question

which of the following is true for all parallelograms? opposite angles are congruent. adjacent sides are congruent. diagonals are congruent. adjacent angles are congruent.

Explanation:

To determine which statement is true for all parallelograms, we analyze each option:

• Opposite angles are congruent: By the definition and properties of a parallelogram, in a parallelogram, opposite angles are equal (congruent). This is a fundamental property of parallelograms.
• Adjacent sides are congruent: In a general parallelogram, adjacent sides are not necessarily congruent. For example, a rectangle is a parallelogram, but adjacent sides (length and width) are congruent only if it is a square. So this is not true for all parallelograms.
• Diagonals are congruent: The diagonals of a parallelogram are congruent only in special cases like rectangles (and squares, which are special rectangles). In a rhombus (a type of parallelogram), diagonals are not congruent (they are perpendicular bisectors of each other). So this is not true for all parallelograms.
• Adjacent angles are congruent: In a parallelogram, adjacent angles are supplementary (their sum is \(180^\circ\)), not necessarily congruent. For example, in a non - rectangular parallelogram (like a rhombus that is not a square), adjacent angles are supplementary but not congruent.

Answer:

Opposite angles are congruent.