Difference between revisions of "Trapezoid"
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| − | + | A '''trapezoid''' is a geometric figure that lies in a plane. It is also a type of [[quadrilateral]]. | |
| − | + | ==Definition== | |
| + | Trapezoids are characterized by having one pair of [[parallel]] sides. Notice that under this definition, every [[parallelogram]] is also a trapezoid. (Careful: some authors insist that a trapezoid must have exactly one pair of parallel sides.) | ||
| − | The two parallel sides of the trapezoid are referred to as the ''bases'' of the trapezoid; the other two sides are called the ''legs''. If the two legs of a trapezoid have equal [[length]], we say it is an [[isosceles trapezoid]]. | + | ==Terminology== |
| + | The two parallel sides of the trapezoid are referred to as the ''bases'' of the trapezoid; the other two sides are called the ''legs''. If the two legs of a trapezoid have equal [[length]], we say it is an [[isosceles trapezoid]]. A trapezoid is cyclic if and only if it is isosceles. | ||
| + | The median of a trapezoid is defined as the line connecting the midpoints of the two legs. Its length is the arithmetic mean of that of the two bases <math>\dfrac{b_1+b_2}{2}</math>. It is also parallel to the two bases. | ||
| − | Given any [[triangle]], a trapezoid can be formed by cutting the triangle with a cut parallel to one of the sides. Similarly, given a trapezoid, one can reconstruct the triangle from which it was cut by extending the legs until they meet. | + | Given any [[triangle]], a trapezoid can be formed by cutting the triangle with a cut parallel to one of the sides. Similarly, given a trapezoid that is not a parallelogram, one can reconstruct the triangle from which it was cut by extending the legs until they meet. |
| − | + | ==Related Formulas== | |
| − | + | If <math>A</math> denotes the area of a trapezoid, <math>b_1,b_2</math> are the two bases, and the perpendicular height is <math>h</math>, we get | |
| + | <cmath>A=\dfrac{h}{2}(b_1+b_2)</cmath> | ||
| + | ==See Also== | ||
| + | *[[Quadrilateral]] | ||
| + | *[[Polygon]] | ||
| + | *[[Parallel]] | ||
| + | |||
| + | [[Category:Definition]] | ||
[[Category:Geometry]] | [[Category:Geometry]] | ||
Revision as of 16:03, 1 February 2022
A trapezoid is a geometric figure that lies in a plane. It is also a type of quadrilateral.
Definition
Trapezoids are characterized by having one pair of parallel sides. Notice that under this definition, every parallelogram is also a trapezoid. (Careful: some authors insist that a trapezoid must have exactly one pair of parallel sides.)
Terminology
The two parallel sides of the trapezoid are referred to as the bases of the trapezoid; the other two sides are called the legs. If the two legs of a trapezoid have equal length, we say it is an isosceles trapezoid. A trapezoid is cyclic if and only if it is isosceles.
The median of a trapezoid is defined as the line connecting the midpoints of the two legs. Its length is the arithmetic mean of that of the two bases 
. It is also parallel to the two bases.
Given any triangle, a trapezoid can be formed by cutting the triangle with a cut parallel to one of the sides. Similarly, given a trapezoid that is not a parallelogram, one can reconstruct the triangle from which it was cut by extending the legs until they meet.
Related Formulas
If 
denotes the area of a trapezoid, 
are the two bases, and the perpendicular height is 
, we get
![\[A=\dfrac{h}{2}(b_1+b_2)\]](http://latex.artofproblemsolving.com/7/1/4/7146502574283e0a452917be1b772223241b6e02.png)
