Math 150

Theorems about Parallelograms

Dr. Wilson

Definition 1: A parallelogram is a four sided figure where the opposite sides are parallel.

Theorem 1: In a parallelogram, the opposite sides are of equal length.

Theorem 2: If the opposite sides in a quadrilateral are the same length, then the figure is a parallelogram.

Theorem 3: A quadrilateral is a parallelogram if and only if the diagonals bisect each other.

Theorem 4: If one pair of opposite sides in a four sided figure are both opposite and parallel, then the figure is a parallelogram.

Definition 2: A rectangle is a quadrilateral where all four angles are the same size.

Theorem 5: A rectangle is a parallelogram.

Theorem 6: A rectangle is a parallelogram if and only if the diagonals are the same length.

Definition 3: A rhombus is a quadrilateral where all four sides have the same length.

Theorem 7: A rhombus is a parallelogram.

Theorem 8: A quadrilateral is a rhombus if and only if the diagonals are perpendicular bisectors of each other.

Theorem 9: A quadrilateral is a rhombus if and only if the diagonals bisect all the vertex angles.

Theorem 10 : If one of the diagonals in a parallelogram bisects one of the vertex angles, then the parallelogram is a rhombus.