![]() Where a and b are the lengths of the parallel sides, h is the height (the perpendicular distance between these sides), and m is the arithmetic mean of the lengths of the two parallel sides. A Lambert quadrilateral in the hyperbolic plane has 3 right angles.įour lengths a, c, b, d can constitute the consecutive sides of a non-parallelogram trapezoid with a and b parallel only when | d − c | < | b − a | < d + c. It is possible for obtuse trapezoids or right trapezoids (rectangles).Ī tangential trapezoid is a trapezoid that has an incircle.Ī Saccheri quadrilateral is similar to a trapezoid in the hyperbolic plane, with two adjacent right angles, while it is a rectangle in the Euclidean plane. A parallelogram has central 2-fold rotational symmetry (or point reflection symmetry). This is possible for acute trapezoids or right trapezoids (as rectangles).Ī parallelogram is (under the inclusive definition) a trapezoid with two pairs of parallel sides. As a consequence the two legs are also of equal length and it has reflection symmetry. Right trapezoids are used in the trapezoidal rule for estimating areas under a curve.Īn acute trapezoid has two adjacent acute angles on its longer base edge.Īn obtuse trapezoid on the other hand has one acute and one obtuse angle on each base.Īn isosceles trapezoid is a trapezoid where the base angles have the same measure. ![]() The orange figures also qualify as parallelograms.Ī right trapezoid (also called right-angled trapezoid) has two adjacent right angles. Rectangles have mirror symmetry on mid-edges rhombuses have mirror symmetry on vertices, while squares have mirror symmetry on both mid-edges and vertices. Under the inclusive definition, all parallelograms (including rhombuses, squares and non-square rectangles) are trapezoids. This is also advocated in the taxonomy of quadrilaterals. This article uses the inclusive definition and considers parallelograms as special cases of a trapezoid. The latter definition is consistent with its uses in higher mathematics such as calculus. Others define a trapezoid as a quadrilateral with at least one pair of parallel sides (the inclusive definition ), making the parallelogram a special type of trapezoid. Some sources use the term proper trapezoid to describe trapezoids under the exclusive definition, analogous to uses of the word proper in some other mathematical objects. Some define a trapezoid as a quadrilateral having only one pair of parallel sides (the exclusive definition), thereby excluding parallelograms. ![]() There is some disagreement whether parallelograms, which have two pairs of parallel sides, should be regarded as trapezoids. Two parallel sides, and no line of symmetry Two parallel sides, and a line of symmetry Opposite sides and angles equal to one another but not equilateral nor right-angled ![]() Proclus (Definitions 30-34, quoting Posidonius) The following is a table comparing usages, with the most specific definitions at the top to the most general at the bottom. This mistake was corrected in British English in about 1875, but was retained in American English into the modern day. no parallel sides – trapezoid (τραπεζοειδή, trapezoeidé, literally trapezium-like ( εἶδος means "resembles"), in the same way as cuboid means cube-like and rhomboid means rhombus-like)Īll European languages follow Proclus's structure as did English until the late 18th century, until an influential mathematical dictionary published by Charles Hutton in 1795 supported without explanation a transposition of the terms. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |