**Trapezium, trapezoid**

A trapezium (UK) or a trapezoid (US)

**A trapezium** is a quadrilateral having two parallel sides of unequal length and the other two sides are non-parallel. The parallel sides of a trapezium are called **bases** **(AD and DC or a and b)** and the non-parallel sides of a trapezium are called **legs (AD and BC or c and d**).

If the legs are equal in length, the trapezoid is called **isosceles**.

The distance between the bases is called the **altitudes of the trapezoid (DE).**

The **midsegment **(FG) of a trapezoid is the segment connecting the midpoints of the two non-parallel sides (AF=FD and BG=GC).

A **trapezoid** is usually considered to be a convex quadrilateral in **Euclidean geometry**, but there are also crossed cases.

**Trapezoid special cases.**

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The orange figures also qualify as parallelograms

A **right trapezoid** (also called right-angled trapezoid) has two adjacent right angles. An **acute trapezoid** has two adjacent acute angles on its longer *base* edge.

An **obtuse trapezoid** on the other hand has one acute and one obtuse angle on each *base*.

An **isosceles trapezoid** is a trapezoid where the base angles have the same measure and the legs are equal in length (AD = BC).

**3-sides equal trapezoid** is a trapezoid with three sides are equal (EH=HG=GF)

A **tangential trapezoid** is a trapezoid that has an **incircle**.

(Source: https://en.wikipedia.org/wiki/Trapezoid)

**Midsegment, a****rea, perimeter **

The length of the **midsegment of trapezoid** is half the sum of the lengths of the two parallel sides.

** a** and

**are the**

*b***lengths**of the parallel sides,

**is the**

*h***height**(the perpendicular distance between these sides),

**is the (**

*m***length of the**

**midsegment)**

**arithmetic mean**of the lengths of the two parallel sides

Tim Brzezinski , LicenseCC-BY-SA, GeoGebra Terms of Use

Tim Brzezinski , LicenseCC-BY-SA, GeoGebra Terms of Use