This fits best with the nature of twentieth-century mathematics. It is possible to function perfectly well with either definition. However, it is important to have agreement in a math class on the definition used in the class. In Math the official definition of a trapezoid is the Inclusive Definition. This narrower view excludes parallelograms as a subset of trapezoids, and leaves only the figures like , , and. Parallelograms with special features, like right angles or all congruent sides or both , are given their own distinctive names: rectangle, rhombus, and square.
The only special feature of a trapezoid that is awarded its own distinctive name is the second pair of parallel sides, which makes the special trapezoid a parallelogram. No other distinctive names are used for trapezoids with special features like right angles or three congruent sides. Shape: Trapezoid. Shape: Trapezoid Topics: Mathematical Language. The horizontal parts are the bases. The last two pieces you drew or put down at the left and right ends are called the trapezoid's legs.
The altitude of a trapezoid is its height. Do not be fooled by the sloping legs -- if they slope, they are longer than the height. Altitude is always measured from the base either parallel side to the other side, at a right angle to the base. You can draw a perpendicular line anywhere along the base of the trapezoid, and when it touches the opposite, parallel side, its length is the altitude. You can identify any trapezoid if it is a quadrilateral with one pair of parallel sides.
Many mathematicians include parallelograms as types of trapezoids because, of course, a parallelogram has at least one pair of parallel sides.
Other mathematicians exclude parallelograms, saying a trapezoid must have exactly one pair of parallel sides. Usually, to be as clear as possible, pictures and drawings of trapezoids show the two parallel sides running horizontally, with the longer side down as the base. Be prepared, though, to see trapezoids in any orientation. A trapezoid can be drawn or pictured with either leg at the bottom, or with the shorter parallel side at the bottom.
Because the parallel sides are the only ones that can be bases, even when the trapezoid is drawn with a leg at the bottom and horizontal, it is not a base. It is still a leg. The base is usually the longer parallel side, but if the trapezoid is drawn with the shorter parallel side at the bottom, then it is the base. Since trapezoids can begin life as triangles, they share names derived from the kinds of triangles:.
A scalene trapezoid has four sides of unequal length. The bases are parallel but of different lengths.
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