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Look up trapezoid in Wiktionary, the free dictionary. In geometry, a trapezoid (/ ˈtræpəzɔɪd /) in North American English, or trapezium (/ trəˈpiːziəm /) in British English, [ 1 ][ 2 ] is a quadrilateral that has one pair of parallel sides. The parallel sides are called the bases of the trapezoid. The other two sides are called the ...
Any non-self-crossing quadrilateral with exactly one axis of symmetry must be either an isosceles trapezoid or a kite. [5] However, if crossings are allowed, the set of symmetric quadrilaterals must be expanded to include also the crossed isosceles trapezoids, crossed quadrilaterals in which the crossed sides are of equal length and the other sides are parallel, and the antiparallelograms ...
Trapezium (UK) or trapezoid (US): at least one pair of opposite sides are parallel. Trapezia (UK) and trapezoids (US) include parallelograms. Isosceles trapezium (UK) or isosceles trapezoid (US): one pair of opposite sides are parallel and the base angles are equal in measure. Alternative definitions are a quadrilateral with an axis of symmetry ...
30-60-90 triangle. Isosceles right triangle. Kepler triangle. Scalene triangle. Quadrilateral – 4 sides. Cyclic quadrilateral. Kite. Parallelogram. Rhombus (equilateral parallelogram)
An antiparallelogram. In geometry, an antiparallelogram is a type of self-crossing quadrilateral. Like a parallelogram, an antiparallelogram has two opposite pairs of equal-length sides, but these pairs of sides are not in general parallel. Instead, each pair of sides is antiparallel with respect to the other, with sides in the longer pair ...
By comparison, a quadrilateral with at least one pair of parallel sides is a trapezoid in American English or a trapezium in British English. The three-dimensional counterpart of a parallelogram is a parallelepiped. The word comes from the Greek παραλληλό-γραμμον, parallēló-grammon, which means a shape "of parallel lines".
If the midpoints of two triangle sides are connected then the resulting line segment is parallel to the third triangle side (Midpoint theorem of triangles). If the midpoints of the two non-parallel sides of a trapezoid are connected, then the resulting line segment is parallel to the other two sides of the trapezoid.
An arbitrary quadrilateral and its diagonals. Bases of similar triangles are parallel to the blue diagonal. Ditto for the red diagonal. The base pairs form a parallelogram with half the area of the quadrilateral, A q, as the sum of the areas of the four large triangles, A l is 2 A q (each of the two pairs reconstructs the quadrilateral) while that of the small triangles, A s is a quarter of A ...