In geometry, what property ensures two opposite sides of a parallelogram are equal and parallel?

• A. Opposite sides of a parallelogram are parallel and congruent.
• B. Opposite angles are supplementary.
• C. Adjacent sides are equal.
• D. Diagonals are perpendicular.

Answer: (A)

In a parallelogram, the two opposite sides are both parallel and congruent. This is because the shape can be seen as a translation, a slide along the plane that carries one side to the opposite side without changing its length or direction. So the opposite sides end up being parallel to each other and equal in length.

Other statements don’t guarantee both properties at once. Opposite angles being supplementary describes the sum of adjacent angles, not the relation of opposite sides. Adjacent sides being equal would make a special case like a rhombus, not every parallelogram. Diagonals being perpendicular happens only in certain parallelograms (like a square or rhombus), not all of them.