A quadrilateral with both pairs of opposite sides
parallel.

Try this Drag the orange dots on each vertex
to reshape the parallelogram. Notice how the opposite sides remain parallel.

A parallelogram is a quadrilateral with opposite sides parallel. But there are various tests that can be applied to see if something is a parallelogram.

It is the "parent" of some other quadrilaterals, which are obtained by adding restrictions of various kinds:

- A rectangle is a parallelogram but with all four interior angles fixed at 90°
- A rhombus is a parallelogram but with all four sides equal in length
- A square is a parallelogram but with all sides equal in length and all interior angles 90°

- Both pairs of opposite sides are parallel. (By definition). Or:
- Both pairs of opposite sides are congruent. If they are congruent, they must also be parallel. Or:
- One pair of opposite sides are congruent
*and*parallel. Then, the other pair must also be parallel.

Base | Any side can be considered a base. Choose any one you like. If used to calculate the area (see below) the corresponding altitude must be used. In the figure above, one of the four possible bases and its corresponding altitude has been chosen. |

Altitude (height) |
The altitude (or height) of a parallelogram is the perpendicular distance from the base to the opposite side (which may have to be extended). In the figure above, the altitude corresponding to the base CD is shown. |

Area | The area of a parallelogram can be found by multiplying a base by the corresponding altitude. See also Area of a Parallelogram |

Perimeter | The distance around the parallelogram. The sum of its sides. See also Perimeter of a Parallelogram |

Opposite sides |
Opposite sides are congruent (equal in length) and parallel. As you reshape the parallelogram at the top of the page, note how the opposite sides are always the same length. |

Diagonals | Each diagonal cuts the other diagonal into two equal parts, as in the diagram below. See Diagonals of a parallelogram for an interactive demonstration of this. |

Interior angles |
Opposite angles are equal as can be seen below. Consecutive angles are always supplementary (add to 180°) For more on both these properties, see Interior angles of a parallelogram. |

If you find the midpoints of each side of any quadrilateral, then link them sequentially with lines, the result is always a parallelogram.

This may seem counter-intuitive at first, but see Parallelogram inscribed in any quadrilateral for an animated exploration of this fact.

- Polygon general definition
- Quadrilateral
- Regular polygon
- Irregular polygon
- Convex polygons
- Concave polygons
- Polygon diagonals
- Polygon triangles
- Apothem of a regular polygon
- Polygon center
- Radius of a regular polygon
- Incircle of a regular polygon
- Incenter of a regular polygon
- Circumcircle of a polygon
- Parallelogram inscribed in a quadrilateral

- Square
- Diagonals of a square
- Rectangle
- Diagonals of a rectangle
- Golden rectangle
- Parallelogram
- Rhombus
- Trapezoid
- Trapezoid median
- Kite
- Inscribed (cyclic) quadrilateral

- Regular polygon area
- Irregular polygon area
- Rhombus area
- Kite area
- Rectangle area
- Area of a square
- Trapezoid area
- Parallelogram area

- Perimeter of a polygon (regular and irregular)
- Perimeter of a triangle
- Perimeter of a rectangle
- Perimeter of a square
- Perimeter of a parallelogram
- Perimeter of a rhombus
- Perimeter of a trapezoid
- Perimeter of a kite

- Exterior angles of a polygon
- Interior angles of a polygon
- Relationship of interior/exterior angles
- Polygon central angle

- Tetragon, 4 sides
- Pentagon, 5 sides
- Hexagon, 6 sides
- Heptagon, 7 sides
- Octagon, 8 sides
- Nonagon Enneagon, 9 sides
- Decagon, 10 sides
- Undecagon, 11 sides
- Dodecagon, 12 sides

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