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- Theorem - A diagonal of a parallelogram divides it into two congruent triangles
- Theorem - In a parallelogram, opposite sides are equal
- Theorem - If each pair of opposite sides of a quadrilateral is equal, then it is a parallelogram
- Theorem - In a parallelogram, opposite angles are equal
- Theorem - If in a quadrilateral, each pair of opposite angles is equal, then it is a parallelogram
- Theorem - The diagonals of a parallelogram bisect each other
- Theorem - If the diagonals of a quadrilateral bisect each other, then it is a parallelogram