Difference between revisions of "Trapezoid"
(property listed) |
m (→Related Formulas: LaTeX tags missing + period) |
||
(11 intermediate revisions by 9 users not shown) | |||
Line 1: | Line 1: | ||
− | + | A '''trapezoid''' is a cool and pretty 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 | ||
+ | <math>A=\dfrac{h}{2}(b_1+b_2)</math>. | ||
+ | ==See Also== | ||
+ | *[[Quadrilateral]] | ||
+ | *[[Polygon]] | ||
+ | *[[Parallel]] | ||
− | + | [[Category:Definition]] | |
− | |||
[[Category:Geometry]] | [[Category:Geometry]] |
Latest revision as of 10:54, 2 January 2024
A trapezoid is a cool and pretty 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
.