Polygon Attributes and Names

One of the most important concepts in studying two-dimensional geometry centers on classification of polygons based on attributes. If you click on the picture, you will see two polygons. One has three sides and one has four sides.

Just counting the number of sides allows us to name the polygons (a triangle and a quadrilateral---If you said, in your head, "square" you are about five steps ahead so slow down :-} ).

Looking at the bottom of the page, notice that the student labeled the vertices (angles) of the polygons. This will allow that student to describe many more attributes of each polygon. In the triangle, line segment BC is congruent to line segment AB. A triangle with at least two congruent line segments is an isosceles triangle. Also, the student should note that angle ABC measures 90 degrees, a right angle. So, this triangle can also be called a right triangle. Putting both attributes together, we get an isosceles right triangle! None of this is possible without close examination of the sides and angles.

In the quadrilateral, please note that the opposites sides are parallel and congruent. This makes our quad a parallelogram. If you notice that all sides are congruent, our parallelogram also becomes a rhombus. If you notice that this parallelogram has four 90 degree angles, then our parallelogram becomes a rectangle. If you notice that our parallelogram has all congruent angles and sides, then we have a regular polygon called a square!

Students are often asked to classify polygons from "least restrictive" name to "most restrictive" name. For our quadrilateral names would include (in order):
polygon
quadrilateral
parallelogram
rectangle
rhombus
square
(rectangle and rhombus could be flip-flopped)

If students were asked to provide attributes of our quadrilateral, they may state:
Our quad has four 90 degree angles
Our quad has opposite sides that are parallel
Our quad has opposite sides that are congruent
Our quad has four lines of symmetry
Our quad has perpendicular line segments...

Please remember that attributes lead to names; they are not the same.


Peace!