In Euclidean plane geometry, a quadrilateral is a polygon with four sides (or edges) and four vertices or corners. Sometimes, the term quadrangle is used, by analogy with triangle, and sometimes tetragon for consistency with pentagon (5-sided), hexagon (6-sided) and so on.
The origin of the word "quadrilateral" is the two Latin words quadri, a variant of four, and latus, meaning "side."
Quadrilaterals are simple (not self-intersecting) or complex (self-intersecting), also called crossed. Simple quadrilaterals are either convex or concave.
The interior angles of a simple (and planar) quadrilateral ABCD add up to 360 degrees of arc, that is
This is a special case of the n-gon interior angle sum formula (n − 2) × 180°. In a crossed quadrilateral, the interior angles on either side of the crossing add up to 720°.
All convex quadrilaterals tile the plane by repeated rotation around the midpoints of their edges.
Read more about Quadrilateral: Convex Quadrilaterals – Parallelograms, Convex Quadrilaterals – Other, More Quadrilaterals, Special Line Segments, Notations in Metric Formulas, Bimedians, Trigonometric Identities, Maximum and Minimum Properties, Remarkable Points and Lines in A Convex Quadrilateral, Other Properties of Convex Quadrilaterals, Taxonomy
Other articles related to "quadrilaterals, quadrilateral":
... Similarly, take the statement "All quadrilaterals have four sides," or equivalently expressed "If a polygon is a quadrilateral, then it has four sides." The ... The inverse is "If a polygon is not a quadrilateral, then it does not have four sides." In this case, unlike the last example, the inverse of the argument is true ... is "If a polygon has four sides, then it is a quadrilateral." Again, in this case, unlike the last example, the converse of the argument is true ...
... A tangential quadrilateral ABCD is a closed figure of four straight sides that are tangent to a given circle C ... Equivalently, the circle C is inscribed in the quadrilateral ABCD ... theorem, the sums of opposite sides of any such quadrilateral are equal, i.e ...
... A taxonomy of quadrilaterals is illustrated by the following graph ... Lower forms are special cases of higher forms ...
... In Euclidean geometry, a tangential quadrilateral (sometimes just tangent quadrilateral) or circumscribed quadrilateral is a convex quadrilateral whose sides are all tangent to a single ... This circle is called the incircle of the quadrilateral or its inscribed circle, its center is the incenter and its radius is called the inradius ... Since these quadrilaterals can be drawn surrounding or circumscribing their incircles, they have also been called circumscribable quadrilaterals, circumscribing ...
... A Saccheri quadrilateral ( Khayyam–Saccheri quadrilateral) is a quadrilateral with two equal sides perpendicular to the base ... The first known consideration of the Saccheri quadrilateral was by Omar Khayyam in the late 11th century, and it may occasionally be referred to as the ... For a Saccheri quadrilateral ABCD, the sides AD and BC (also called legs) are equal in length and perpendicular to the base AB ...