parallelogram
Sign in to saveIn Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. The congruence of opposite sides and opposite angles is a direct consequence of the Euclidean parallel postulate and neither condition can be proven without appealing to the Euclidean parallel postulate or one of its equivalent formulations.
AI overview
A parallelogram is a four-sided shape where opposite sides are parallel to each other, which automatically makes those opposite sides equal in length and opposite angles equal in size. This shape is fundamental to Euclidean geometry because its defining properties depend directly on the parallel postulate, a cornerstone assumption of how geometry works in flat space.
AI-generated from the Wikipedia summary — may contain errors.
Key facts
- Polygon.name
- Parallelogram
- Polygon.image
- Parallelogram.svg
- Polygon.caption
- This parallelogram is a rhomboid as it has unequal sides and no right angles.
- Polygon.type
- Quadrilateral, Trapezium
- Polygon.edges
- 4
- Polygon.symmetry
- C2, [2]+,
- Polygon.area
- bh (base × height);ab sin θ (product of adjacent sides and sine of the vertex angle determined by them)
- Polygon.properties
- Convex polygon
via Wikipedia infobox
Article
15 sectionsContents
- Special cases
- Characterizations
- Other properties
- Area formula{{anchor|Area}}
- From vertex coordinates
- Proof that diagonals bisect each other
- Lattice of parallelograms
- Parallelograms arising from other figures
- Automedian triangle
- Varignon parallelogram
- Tangent parallelogram of an ellipse
- Faces of a parallelepiped
- See also
- References
- External links
In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. The congruence of opposite sides and opposite angles is a direct consequence of the Euclidean parallel postulate and neither condition can be proven without appealing to the Euclidean parallel postulate or one of its equivalent formulations.
By comparison, a quadrilateral with at least one pair of parallel sides is a trapezoid in American English or a trapezium in British English.