Students define a parallelogram, explore the properties of a parallelogram and their proofs, and use these properties to solve problems
After completing this tutorial, you will be able to complete the following:
Recall that a quadrilateral is a four-sided polygon. A parallelogram is a quadrilateral with opposite sides parallel. This figure is one of the most fundamental types of quadrilaterals. In fact, several other types of quadrilaterals such as rhombuses, rectangles, and squares are parallelograms with special properties. The hierarchy of quadrilaterals is shown in Figure 1.
The term "parallelogram" derives from the Greek word meaning a shape of "parallel lines." This etymology reflects the definition. The line containing any side of a parallelogram forms a transversal of two lines containing opposite, parallel sides. As a result, the following properties follow directly from the definition of parallelogram and Euclid's Parallel Postulate or one of its equivalent forms:
|Approximate Time||20 Minutes|
|Pre-requisite Concepts||Students should be able to define congruency and quadrilateral; explain the properties of a quadrilateral; identify the bisectors, diagonals, and angles of a quadrilateral; understand triangles by side-angle-side, angle-side-angle, and side-side-side congruency; identify the angles formed by two parallel lines intersected by a transversal; and understand the theorems involving lines intersected by a transversal.|
|Type of Tutorial||Concept Development|
|Key Vocabulary||bisect, consecutive angles, diagonal|