Parallelogram in Geometry: Definition, Shapes & Properties

Parallelogram in Geometry: Definition, Shapes & Properties
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  • 0:01 What Is a Parallelogram?
  • 1:02 Properties
  • 1:39 Lesson Summary
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Lesson Transcript
Instructor: Cathryn Jackson

Cat has taught a variety of subjects, including communications, mathematics, and technology. Cat has a master's degree in education and is currently working on her Ph.D.

Parallelograms appear in many places in everyday life. Identify the shapes and properties of a parallelogram in this lesson, and review what you've learned with a short quiz.

What Is a Parallelogram?

A parallelogram is just as the name implies. It has two pairs of sides that are parallel. A parallelogram has four sides total. The most recognizable parallelogram is the square; however, a parallelogram can be many shapes:

  • A square is the parallelogram that has four equal sides. The opposite sides are parallel and all corners of the square form a right angle.
  • A rectangle is a parallelogram that has four opposite, parallel, congruent sides. The corners of the rectangle form a right angle. The only difference between a rectangle and a square is that the rectangle sides are not all equal.
  • A rhombus has four equal sides. The opposite sides are parallel, but the corners do not form right angles. A diamond shape is a good example of a rhombus.
  • A rhomboid has four parallel sides. The opposite sides are equal, but the corners do not form right angles. Think of a rectangle that is slanted.

Parallelograms shapes
Parallelograms

Properties

These properties of parallelograms will help you identify parallelograms and solve geometric problems:

  • Parallelograms will always have parallel sides - if the sides continued forever, they would never touch or intersect one another.
  • If you draw a diagonal line from corner to corner in a parallelogram, the diagonal lines would intersect one another to create bisecting lines.

Bisecting lines in parallelograms
Parallelograms

  • Parallelograms will have at least one pair of opposite sides that are congruent, or of equal length.
  • Parallelograms will also have at least one pair of opposite angles that are congruent.

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