Trapezoid - Revision history

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2025-04-26T20:38:19Z

Historical Context

← Older revision		Revision as of 20:38, 26 April 2025
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	== Historical Context ==		== Historical Context ==

	~~[[File:Trapezium_and_Trapezoid,_Hutton s_mistake_in_1795.png\|Historical depiction of trapezoid terminology\|thumb\|left]]~~

	The terminology surrounding trapezoids has varied historically and geographically. In British English, the term "trapezium" is often used to describe what is known as a trapezoid in American English, and vice versa. This discrepancy has led to some confusion in mathematical literature.		The terminology surrounding trapezoids has varied historically and geographically. In British English, the term "trapezium" is often used to describe what is known as a trapezoid in American English, and vice versa. This discrepancy has led to some confusion in mathematical literature.

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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."
+A '''trapezoid''' is a [[quadrilateral]] with at least one pair of parallel sides. In the context of [[geometry]], trapezoids are a fundamental shape studied for their unique properties and applications in various fields such as architecture, engineering, and mathematics.
-== Properties ==
+[[File:Trapezoid.svg|Diagram of a trapezoid|thumb|right]]
-A trapezoid has several important properties:
+== Definition and 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.
+In [[Euclidean geometry]], a trapezoid is defined as a four-sided figure, or quadrilateral, with at least one pair of parallel sides. These parallel sides are referred to as the "bases" of the trapezoid, while the non-parallel sides are called the "legs." The height of a trapezoid is the perpendicular distance between the bases.
-== Special Cases ==
+The area of a trapezoid can be calculated using the formula:
-* A [[parallelogram]] is a special case of a trapezoid where both pairs of opposite sides are parallel.
+: \( A = \frac{1}{2} \times (b_1 + b_2) \times h \)
-== Etymology ==
+where \( b_1 \) and \( b_2 \) are the lengths of the two parallel sides, and \( h \) is the height.
-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.
+== Types of Trapezoids ==
 == Related Pages ==
@@ Line 25: / Line 45: @@
 * [[Quadrilateral]]
 * [[Parallelogram]]
 * [[Rectangle]]
-* [[Square]]
+* [[Trapezium]]
-* [[Rhombus]]
-== References ==
+[[File:Trapezoid_3_(PSF).png|Trapezoid with labeled angles|thumb|left]]
-{{Reflist}}
+== Notes ==
-== Gallery ==
+The distinction between trapezoid and trapezium is important in understanding the geometric properties and applications of these shapes. The use of these terms can vary, so it is essential to clarify the context in which they are used.
-<gallery>
+[[File:Trapezium_(PSF).png|Trapezium in British English|thumb|right]]
 [[Category:Quadrilaterals]]

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 File:Trapezium.svg|Trapezoid
 File:Temple_of_Dendur-_night.jpg|Trapezoid
 </gallery>

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← Older revision		Revision as of 12:13, 18 February 2025
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	[[Category:Quadrilaterals]]		[[Category:Quadrilaterals]]
			<gallery>
			File:Trapezoid.svg\|Trapezoid
			File:Trapezium_and_Trapezoid,_Hutton’s_mistake_in_1795.png\|Trapezium and Trapezoid, Hutton’s mistake in 1795
			File:Rhombus_2_(PSF).png\|Trapezoid
			File:Rhomboid_2_(PSF).png\|Trapezoid
			File:Trapezoid_2_(PSF).png\|Trapezoid
			File:Trapezoid_3_(PSF).png\|Trapezoid
			File:Trapezium_(PSF).png\|Trapezoid
			File:Trapezoid_special_cases.png\|Trapezoid special cases
			File:Trapez_mittellinie_en_labels.svg\|Trapezoid
			File:Trapez_mittellinie_en_labels_areas.svg\|Trapezoid
			File:Trapezium.svg\|Trapezoid
			File:Temple_of_Dendur-_night.jpg\|Trapezoid
			</gallery>

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← Older revision		Revision as of 00:35, 10 February 2025
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	~~'''~~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]]		* [[Quadrilateral]]
	* [[Polygon]]
	* [[Parallelogram]]		* [[Parallelogram]]
	* [[Rectangle]]		* [[Rectangle]]
			* [[Square]]
	* [[Rhombus]]		* [[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:Quadrilaterals]]
	~~[[Category:Elementary geometry]]~~

	~~{{stub}}~~

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New page

'''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.

==Etymology==
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 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==
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.

==Properties==
The properties of the trapezoid are as follows:
* The bases are parallel by definition.
* If the legs are equal in length, then the base angles are equal. This is the definition of an isosceles trapezoid.
* The diagonals of a trapezoid bisect each other.
* The sum of the interior angles of a trapezoid is 360 degrees.

==See also==
* [[Quadrilateral]]
* [[Polygon]]
* [[Parallelogram]]
* [[Rectangle]]
* [[Rhombus]]
* [[Square]]

[[Category:Quadrilaterals]]
[[Category:Elementary geometry]]

{{stub}}