Students define a trapezoid, explore its properties and their proofs, and use these properties to solve problems.
After completing this tutorial, you will be able to complete the following:
Trapezoids are quadrilaterals with one pair of parallel sides. There has been some debate about the number of parallel sides allowed in a trapezoid. If a trapezoid is defined as having at least one pair of parallel sides, then all parallelograms would also be considered to be trapezoids. However, it is more common for trapezoids to be defined as having exactly one pair of parallel sides, and this is the definition applied here. As a result, the hierarchy of quadrilaterals is as follows:
Trapezoids derive their name from the ancient Greek "trapezion," meaning "little table," and are sometimes called "trapeziums" in countries outside North America.
When describing a trapezoid, we use the following definitions:
The legs of a trapezoid are transversals of the bases and many of the properties of a trapezoid are derived from this fact along with facts about triangles.
Properties of a trapezoid:
|Approximate Time||20 Minutes|
|Pre-requisite Concepts||Students should be able to define and explain the properties of a quadrilateral; identify the diagonal of a quadrilateral; understand the angle-side-angle congruency, angle-angle similarity, and triangle midsegment theorems; and identify corresponding and supplementary angles.|
|Type of Tutorial||Concept Development|
|Key Vocabulary||base of a trapezoid, trapezoid, interior angles of a trapezoid|