Tetragon
In geometry a quadrilateral is a four-sided polygon, having four edges (sides) and four corners (vertices). The word is derived from the Latin words quadri, a variant of four, and latus, meaning "side". It is also called a tetragon, derived from Greek "tetra" meaning "four" and "gon" meaning "corner" or "angle", in analogy to other polygons (e.g. pentagon). Since "gon" means "angle", it is analogously called a quadrangle, or 4-angle. A quadrilateral with vertices
A
{\displaystyle A}
,
B
{\displaystyle B}
,
C
{\displaystyle C}
and
D
{\displaystyle D}
is sometimes denoted as
◻
A
B
C
D
{\displaystyle \square ABCD}
.
Quadrilaterals are either simple (not self-intersecting), or complex (self-intersecting, or crossed). Simple quadrilaterals are either convex or concave.
The interior angles of a simple (and planar) quadrilateral ABCD add up to 360 degrees, that is
∠
A
+
∠
B
+
∠
C
+
∠
D
=
360
∘
.
{\displaystyle \angle A+\angle B+\angle C+\angle D=360^{\circ }.}
This is a special case of the n-gon interior angle sum formula: S = (n − 2) × 180° (here, n=4).
All non-self-crossing quadrilaterals tile the plane, by repeated rotation around the midpoints of their edges.
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