Difference between revisions of "Trapezoid"
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==Definition== | ==Definition== | ||
| − | Trapezoids are characterized by having one pair of [[parallel]] sides. | + | 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== | ==Terminology== | ||
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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. | 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== | ==Related Formulas== | ||
Revision as of 15:03, 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)
