What clusters of polygons will tessellate a plane?

Certain clusters of polygons will tessellate a plane when 2 or more polygons are used together. In this part of the lesson, you will use an interactive geometry applet to explore some clusters of polygons that tessellate.

Click on this link

The top bar of this applet contains different polygons. Click on a polygon several times to get several copies of that polygon in the sketch window. Drag the polygons to see if you can arrange them so that they are non-overlapping and that their vertices line up without leaving any gaps. If you can, then the polygon tessellates. Do this for each polygon in the chart below.

Use your results to fill in a chart like the one shown below.

(Move your mouse over the table to see answers.)

Pause and Reflect

Look at the data in the chart. Which clusters of polygons tessellated? What relationship do the sums of the measures of the interior angles of the polygons that tessellated have to 360^o?

Interactive popup. Assistance may be required.

A cluster of polygons will tessellate if some combination of those polygons has a sum of interior angles at one vertex equal to 360^o. If the polygons cannot be arranged so that their adjacent interior angles will sum to 360^o, then the cluster of polygons will not tessellate.