Polygons and Quadrilaterals

by Laurie Laurendeau on March 6, 2012

A polygon is a closed figure whose sides are all line segments.  A polygon cannot have curved sides.  Examples of polygons include a triangle, square, rectangle, or any unnamed shape that is closed in, and has straight sides.  A circle is not a polygon.  A quadrilateral is a special kind of polygon that has exactly four sides that are all line segments.  This means that a quadrilateral always has 4 sides, 4 angles, the sides cannot be curved, and the figure must be closed in (because it is a type of polygon).  So, a quadrilateral is always a polygon, but a polygon is not always a quadrilateral.  Are you lost yet?!

Students learn to classify shapes as early as 2nd grade.  They often get confused because shapes end up having a lot of different names.  I tell them that the word Polygon is at the top of the list, and then we can classify even more specifically under that.  So, a square is first a polygon, it is more specifically a quadrilateral, more specifically it is a parallelogram, and even more specifically, it is a square.   I compare this to saying that I am a human being, but more specifically, I am a female.  All human beings are not female, but all females are human beings.

Classifying Quadrilaterals

Some quadrilaterals have special characteristics, therefore we can classify them more specifically and we give them special names.

  1. Parallelogram: A parallelogram is a quadrilateral whose opposite sides are the same length, and they are parallel.  Examples of parallelograms include a square, rectangle, rhombus, etc.
  2. Rectangle: A rectangle is a parallelogram with 4 right angles.  Therefore, what we commonly think of as a rectangle is of course a rectangle, but a square is also a rectangle by definition.
  3. Rhombus: A rhombus is a parallelogram with all 4 sides the same length.  Therefore, a square is technically also a rhombus.
  4. Square: A square is a type of rectangle that has 4 sides that are equal length, and has 4 right angles.
  5. Trapezoid: A trapezoid is a quadrilateral that has exactly one pair of parallel sides.


  • As always, playing math games at home is a great way to reinforce math skills learned in school.
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