# Geometry/Trapezoids

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A **Trapezoid** (American English) or **Trapezium** (British English) is a quadrilateral that has two parallel sides and two non parallel sides.

Some properties of trapezoids:

- The interior angles sum to 360° as in any quadrilateral.
- The parallel sides are unequal.
- Each of the parallel sides is called a
*base (b)*of the trapezoid. The two angles that join one base are called 'base angles'. - If the two non-parallel sides are equal, the trapezoid is called an
*isosceles trapezoid*.- In an isosceles trapezoid, each pair of base angles are equal.
- If one pair of base angles of a trapezoid are equal, the trapezoid is isosceles.

- A line segment connecting the midpoints of the non-parallel sides is called the
*median (m)*of the trapeziod.- The median of a trapezoid is equal to one half the sum of the bases (called
*b*and_{1}*b*)._{2}

- The median of a trapezoid is equal to one half the sum of the bases (called
- A line segment perpendicular to the bases is called an
*altitude (h)*of the trapezoid.

The *area (A)* of a trapezoid is equal to the product of an altitude and the median.

Recall though that the median is half of the sum of the bases.

Substituting for m, we get: