Students define an isosceles 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:
Some properties of a trapezoid:
An isosceles trapezoid is a trapezoid whose legs are congruent. Isosceles trapezoids have some additional properties:
Trapezoids with the following properties are isosceles:
angles on the same base are congruent and the diagonals divide each other into congruent line segments.
|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; define a trapezoid, its bases, and its legs; explain the properties of a trapezoid; understand angle-side-angle congruency, angle-angle similarity, and the triangle midsegment theorem; and identify corresponding angles and supplementary angles.|
|Type of Tutorial||Concept Development|
|Key Vocabulary||base of an isosceles trapezoid, congruent angles, isosceles trapezoid|