Does a Trapezoid have one pair of parallel sides?
In North America, a trapezium with at least one pair of parallel sides is referred to as a trapezoid.There are two pairs of bases if the legs and the parallel sides are not parallel.In contrast to the special cases below, a scalene trapezoid has no sides of equal measure.
The term trapezium has been used in English since 1570.[5]
The first recorded use of the Greek word translated was by Marinus Proclus in his commentary on the first book of Euclid's Elements.[5]
The term is used in the United States and Canada.The form used in many languages is the one closest to trapezium, not the other way around.Spanish trapecio, German trapez, and French trapze are examples.
There were no parallel sides in Britain and other countries when the term was first used.The Oxford English Dictionary says "often called by English writers in the 19th century".According to the OED, the meaning of the term "trapezoid" is the sense of a figure with no sides parallel.The French trapézode, German trapezoid, and other languages retain this.This sense is no longer relevant.
A trapezium has one pair of its opposite sides parallel.This was the specific sense in England in the 17th and 18th centuries, and again in recent use outside of North America.The sense of a trapezium is more general than a parallelogram.
There was a time when the word trapezium was used in England.This is still going on in North America.This shape is called an irregular quadrilateral.[8]
Some people disagree about whether parallelograms, which have two pairs of parallel sides, should be regarded as trapezoids.The exclusive definition of a trapezoid is one with only one pair of parallel sides.The parallelogram is a special type of trapezoid because it has at least one pair of parallel sides.The latter definition is used in higher mathematics.Parallelograms are considered to be special cases of a trapezoid.This is also advocated in the quadrilaterals.
All parallelograms are trapezoids under the inclusive definition.rhombuses and squares have mirror symmetry on their mid-edges.
There are two right angles to a right trapezoid.The trapezoidal rule is used to estimate areas under a curve.
An acute trapezoid has two adjacent acute angles on its longer base edge, while an twinning has one acute and one obtuse angle on each base.
The base angles of a isosceles trapezoid have the same measure.The two legs have the same length and reflection symmetry.This can be done for acute and right trapezoids.
A parallelogram has two parallel sides.There is a point reflection symmetry in a parallelogram.It's possible for right and left trapezoids.
A Saccheri quadrilateral is similar to a trapezoid in the hyperbolic plane with two adjacent right angles.The hyperbolic plane has 3 right angles.
Four lengths a, c, b, d can be used to form the sides of a non-parallelogram trapezoid.
The ex-tangential quadrilateral is not a parallelogram when d c is b.35
The following properties imply that the quadrilateral is a trapezoid.
The following properties imply that the opposite sides are parallel.
The segment that joins the legs is called the median or midline.The bases are parallel to it.Its length is the same as the average lengths of the bases.
One of the two bimedians divides the trapezoid into equal areas.
The altitude is the distance between the bases.The height of a trapezoid can be determined by the length of its four sides using the formula if the two bases have different lengths.
When a and b are the lengths of the parallel sides, h is the height and m the mean.In 499 AD, a great mathematician-astronomer from the classical age of Indian mathematics and Indian astronomy used this method.The formula for the area of a triangle is well-known, so it makes sense that this formula would be used for a degenerate triangle in which one of the parallel sides has shrunk to a point.
The 7th-century Indian mathematician Bhskara I came up with a formula for the area of a trapezoid with consecutive sides.
Where a and b are parallel.This formula can be used in a more symmetric version.
When one of the parallel sides has shrunk to a point, this formula reduces to Heron's formula for the area of a triangle.
The semiperimeter of the trapezoid is where s is.The formula is similar to the one used by the author, but it is different in that a trapezoid might not be in a circle.The formula is a special case for a general quadrilateral.
If the trapezoid is divided into four triangles by its diagonals, the area is equal to that of the triangle.The areas of each pair of triangles are the same as the lengths of the parallel sides.[2]
A, B, C, and D are in sequence and have parallel sides.Let E be the intersection of the diagonals and allow F and G to be on the opposite sides of BC.FG is the mean of DC andAB.
Each base is divided by the line that goes through the intersection points of the extended nonparallel sides and the diagonals.[17]
The center of area is along the line segment joining the parallel sides at a distance from the longer side.
When taken from the short to the long side, this segment is divided by the center of the area.