Which statement is true for a parallelogram?

Which statement is true for a parallelogram?

• A. Opposite sides are congruent
• B. All sides are congruent
• C. Diagonals are always perpendicular
• D. Adjacent sides are perpendicular

Answer: (A)

Opposite sides of a parallelogram are congruent because the figure has two pairs of parallel sides. When a side is shifted along the direction of the opposite side, it lines up exactly with that opposite side, showing they have the same length. This equality of opposite sides holds for every parallelogram, regardless of the angles. The other statements aren’t guaranteed in a general parallelogram: all sides being congruent would make a rhombus, not every parallelogram; diagonals are not always perpendicular (that happens in special cases like a rhombus); and adjacent sides being perpendicular would give a rectangle, which is a parallelogram but not the defining property.

Opposite sides of a parallelogram are congruent because the figure has two pairs of parallel sides. When a side is shifted along the direction of the opposite side, it lines up exactly with that opposite side, showing they have the same length. This equality of opposite sides holds for every parallelogram, regardless of the angles.

The other statements aren’t guaranteed in a general parallelogram: all sides being congruent would make a rhombus, not every parallelogram; diagonals are not always perpendicular (that happens in special cases like a rhombus); and adjacent sides being perpendicular would give a rectangle, which is a parallelogram but not the defining property.