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Parallelogram and Its Properties

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Quadrilaterals

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Parallelogram and Its Properties

Geometry

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Students define a parallelogram, explore the properties of a parallelogram and their proofs, and use these properties to solve problems

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Now You Know

After completing this tutorial, you will be able to complete the following:

  • After completing this Activity Object, students will be able to:
  • Define a parallelogram as a quadrilateral with opposite sides parallel.
  • Explain the properties of a parallelogram: opposite sides are congruent, opposite angles are congruent, diagonals bisect each other, and consecutive interior angles are supplementary.
  • Apply the properties of a parallelogram.

Everything You'll Have Covered

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:

  • Opposite sides of a parallelogram are congruent.
  • Opposite angles of a parallelogram are congruent.
  • The diagonals of a parallelogram bisect each other.
  • Consecutive interior angles of a parallelogram are supplementary.

Tutorial Details

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.
Course Geometry
Type of Tutorial Concept Development
Key Vocabulary bisect, consecutive angles, diagonal