Organizing the Relationships
between Different Types of Parallelograms

by David Wise

Note: I recommend that this page be printed out, so that the instructions are easier to follow.

A Venn Diagram:

A Family Tree:

These two diagrams visually display the relationships between different types of parallelograms based upon their definition. To help solidify the relationships, I recommend that you sketch the Venn Diagram and/or the family tree. Within the sketch, list the definition and the properties of each figure.

The above sketches should be interpreted in the following manner.
All parallelograms are quadrilaterals.
All rhombuses are parallelograms, and therefore are also quadrilaterals.
All rectangles are parallelograms, and therefore are also quadrilaterals.
All squares are rhombuses and rectangles, and therefore are also parallelograms and quadrilaterals.

Quadrilaterals are the most general geometric figure, while squares are the most specialized. Therefore, all of the properties of a figure include all of the properties of the geometric figure(s) preceeding (or surrounding) it. The following are links to investigations of properties of parallelograms.

Parallelograms

Rhombuses

Rectangles

Squares

If you have any questions while trying to complete this investigation, or suggestions that would be useful, especially for use at the high school level, please send e-mail to esiwdivad@yahoo.com.

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