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Isosceles trapezoid  Wikipedia, the free encyclopedia

** Isosceles trapezoid **
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Isosceles trapezoid
Isosceles trapezoid.svgIsosceles trapezoid with axis of symmetry
Type quadrilateral, trapezoid
Edges and vertices 4
Symmetry group Dih[2], [ ], (*), order 2
Dual polygon Kite
Properties convex, cyclic
In Euclidean geometry, an *isosceles trapezoid* (*isosceles trapezium* in
British English) is a convex quadrilateral with a line of symmetry
bisecting one pair of opposite sides. It is a special case of a trapezoid.
In any isosceles trapezoid two opposite sides (the bases) are parallel, and
the two other sides (the legs) are of equal length (properties shared with
the parallelogram). The diagonals are also of equal length. The base angles
of an isosceles trapezoid are equal in measure (there are in fact two pairs
of equal base angles, where one base angle is the supplementary angle of a
base angle at the other base).
*Contents*
· 1 Special cases
· 1.1 Selfintersections
· 2 Characterizations
· 3 Angles
· 4 Diagonals and height
· 5 Area
· 6 Circumradius
· 7 See also
· 8 References
· 9 External links
*Special cases[edit]*
Special cases of isosceles trapezoids
Rectangles and squares are usually considered to be special cases of
isosceles trapezoids though some sources would exclude them.
Another special case is a /3equal side trapezoid/, sometimes known as a
/trilateral trapezoid/^[1] or a /trisosceles trapezoid/.^[2] They can also
be seen dissected from regular polygons of 5 sides or more as a truncation
of 4 sequential vertices.
The isosceles trapezoid is also rarely known as a /symtra/ because of its
symmetry.^[3]
Selfintersections[edit]
Any nonselfcrossing quadrilateral with exactly one axis of symmetry must
be either an isosceles trapezoid or a kite.^[3] However, if crossings are
allowed
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