Trapezoid: Difference between revisions

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Trapezoid

A trapezoid is a quadrilateral with at least one pair of parallel sides. In British English, the term "trapezium" is often used to refer to this shape, while in American English, "trapezium" refers to a quadrilateral with no parallel sides. The parallel sides are referred to as the "bases" of the trapezoid, and the non-parallel sides are called the "legs."

Properties

A trapezoid has several important properties:

The midsegment (or median) of a trapezoid is parallel to the bases and its length is the average of the lengths of the bases.
The area of a trapezoid can be calculated using the formula: \( A = \frac{1}{2} \times (b_1 + b_2) \times h \), where \( b_1 \) and \( b_2 \) are the lengths of the two bases, and \( h \) is the height (the perpendicular distance between the bases).
If the legs of the trapezoid are equal in length, the trapezoid is called an isosceles trapezoid. An isosceles trapezoid has additional properties, such as equal angles adjacent to each base and equal diagonals.

Special Cases

A parallelogram is a special case of a trapezoid where both pairs of opposite sides are parallel.
A rectangle is a trapezoid with right angles.
A square is a trapezoid with equal sides and right angles.

Etymology

The word "trapezoid" comes from the Greek word "trapezion," meaning "little table," which is derived from "trapeza," meaning "table." The term reflects the shape's resemblance to a table.

Related Pages

References

Gallery

Diagram of a trapezoid
Comparison with a rhombus
Comparison with a rhomboid
Another trapezoid example
Trapezoid with labeled angles
Trapezium in British English
Special cases of trapezoids
Trapezoid with midsegment labeled
Trapezoid with area calculation
Trapezium in American English

@@ Line 1: / Line 1: @@
-'''Trapezoid'''
+== Trapezoid ==
-A '''trapezoid''' in [[American English]] or a '''trapezium''' in [[British English]] is a [[convex quadrilateral]] with at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid and the other two sides are called the legs or the lateral sides.
+A '''trapezoid''' is a [[quadrilateral]] with at least one pair of parallel sides. In [[British English]], the term "trapezium" is often used to refer to this shape, while in [[American English]], "trapezium" refers to a quadrilateral with no parallel sides. The parallel sides are referred to as the "bases" of the trapezoid, and the non-parallel sides are called the "legs."
-==Etymology==
+== Properties ==
-The term trapezoid was first used in English in 1570, from the [[Greek language|Greek]] ''trapezoeides'' which means "table-like", from ''trapeza'' for "table" + ''-oeides'' for "shape".
-==Characteristics==
+A trapezoid has several important properties:
-A trapezoid is a quadrilateral with exactly one pair of parallel sides. The parallel sides are called the bases of the trapezoid, and the other two sides are called the legs. The base angles of a trapezoid are the angles on the same base of the trapezoid.
-==Types of Trapezoids==
+* The [[midsegment]] (or median) of a trapezoid is parallel to the bases and its length is the average of the lengths of the bases.
-There are two types of trapezoids: right trapezoids and isosceles trapezoids. A '''right trapezoid''' has two adjacent right angles. An '''isosceles trapezoid''' has base angles that are equal, and therefore it has two pairs of adjacent sides that are equal in length.
+* The area of a trapezoid can be calculated using the formula: \( A = \frac{1}{2} \times (b_1 + b_2) \times h \), where \( b_1 \) and \( b_2 \) are the lengths of the two bases, and \( h \) is the height (the perpendicular distance between the bases).
+* If the legs of the trapezoid are equal in length, the trapezoid is called an [[isosceles trapezoid]]. An isosceles trapezoid has additional properties, such as equal angles adjacent to each base and equal diagonals.
-==Properties==
+== Special Cases ==
-The properties of the trapezoid are as follows:
-* The bases are parallel by definition.
+* A [[parallelogram]] is a special case of a trapezoid where both pairs of opposite sides are parallel.
-* If the legs are equal in length, then the base angles are equal. This is the definition of an isosceles trapezoid.
+* A [[rectangle]] is a trapezoid with right angles.
-* The diagonals of a trapezoid bisect each other.
+* A [[square]] is a trapezoid with equal sides and right angles.
-* The sum of the interior angles of a trapezoid is 360 degrees.
+== Etymology ==
+The word "trapezoid" comes from the Greek word "trapezion," meaning "little table," which is derived from "trapeza," meaning "table." The term reflects the shape's resemblance to a table.
+== Related Pages ==
-==See also==
 * [[Quadrilateral]]
-* [[Polygon]]
 * [[Parallelogram]]
 * [[Rectangle]]
+* [[Square]]
 * [[Rhombus]]
-* [[Square]]
+== References ==
+{{Reflist}}
+== Gallery ==
+<gallery>
+File:Trapezoid.svg|Diagram of a trapezoid
+File:Rhombus_2_(PSF).png|Comparison with a rhombus
+File:Rhomboid_2_(PSF).png|Comparison with a rhomboid
+File:Trapezoid_2_(PSF).png|Another trapezoid example
+File:Trapezoid_3_(PSF).png|Trapezoid with labeled angles
+File:Trapezium_(PSF).png|Trapezium in British English
+File:Trapezoid_special_cases.png|Special cases of trapezoids
+File:Trapez_mittellinie_en_labels.svg|Trapezoid with midsegment labeled
+File:Trapez_mittellinie_en_labels_areas.svg|Trapezoid with area calculation
+File:Trapezium.svg|Trapezium in American English
+</gallery>
 [[Category:Quadrilaterals]]
-[[Category:Elementary geometry]]
-{{stub}}