# Geometry/Trapezoids

From Wikibooks, open books for an open world

< Geometry

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:

- Chapter 2. Geometry/Angles
- Chapter 3. Geometry/Properties
- Chapter 4. Geometry/Inductive and Deductive Reasoning
- Chapter 5. Geometry/Proof
- Chapter 6. Geometry/Five Postulates of Euclidean Geometry
- Chapter 7. Geometry/Vertical Angles
- Chapter 8. Geometry/Parallel and Perpendicular Lines and Planes
- Chapter 9. Geometry/Congruency and Similarity
- Chapter 10. Geometry/Congruent Triangles
- Chapter 11. Geometry/Similar Triangles
- Chapter 12. Geometry/Quadrilaterals
- Chapter 13. Geometry/Parallelograms
- Chapter 14. Geometry/Trapezoids
- Chapter 15. Geometry/Circles/Radii, Chords and Diameters
- Chapter 16. Geometry/Circles/Arcs
- Chapter 17. Geometry/Circles/Tangents and Secants
- Chapter 18. Geometry/Circles/Sectors
- Appendix A. Geometry/Postulates & Definitions
- Appendix B. Geometry/The SMSG Postulates for Euclidean Geometry

- Part II- Coordinate Geometry:

- Two and Three-Dimensional Geometry and Other Geometric Figures
- Geometry/Perimeter and Arclength
- Geometry/Area
- Geometry/Volume
- Geometry/Polygons
- Geometry/Triangles
- Geometry/Right Triangles and Pythagorean Theorem
- Geometry/Polyominoes
- Geometry/Ellipses
- Geometry/2-Dimensional Functions
- Geometry/3-Dimensional Functions
- Geometry/Area Shapes Extended into 3rd Dimension
- Geometry/Area Shapes Extended into 3rd Dimension Linearly to a Line or Point
- Geometry/Polyhedras
- Geometry/Ellipsoids and Spheres
- Geometry/Coordinate Systems (currently incorrectly linked to Astronomy)

- Traditional Geometry:

- Modern geometry