Tessellations Worksheet (Page 3 of 4) in pdf

Project AMP

Dr. Antonio Quesada – Director, Project AMP

b. Rotate the triangle about any midpoint 180

. Refer to appendix to recall

this procedure. Continue this process until the screen is filled or the

polygons overlap.

[Use Midpoint, Numerical Edit, and Rotate tools.]

Does the triangle tessellate? Explain your conclusions using your

knowledge of the sum of the interior angles of a triangle.

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2. Draw a convex or concave quadrilateral.

a. Follow the same process described in #1.

b. Does the quadrilateral tessellate? Explain your conclusions using by using

your knowledge of the sum of the interior angles of a quadrilateral.

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3. It is possible for some pentagons to tessellate. Repeat the previous process for a

pentagon. If the pentagon you create does not tessellate, change the shape using

the hand tool until the pentagon does tessellate. When creating the pentagon,

label the vertices to distinguish the original pentagon.

Why do some pentagons tessellate when others do not?

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Appendix:

To create a regular triangle, select the Regular Polygon tool. Click on the screen to

create the center point. Rotate your mouse clockwise until a regular triangle appears,

then click. Select the Numerical Edit tool from the display toolbox. Type in the interior

angle measure of the regular polygon. Press CRTL + U and select the degrees unit.

Select the Rotate tool from the transform toolbox. Click on the polygon, click on the

angle measure, then click on one of the vertices of the polygon. Repeat this process on

the newly constructed polygon.

To rotate the polygon 180

about a midpoint, select the Numerical Edit tool from the

display toolbox. Type in the value 180. Press CTRL + U to see a list of units. Select

degrees. Select the Rotate tool from the transform toolbox. Click on the polygon, click

on the numerical value, then click on the midpoint of any side. Repeat the process by

finding the midpoint of one of the new sides created and rotating about that point.

Extension

Your grandmother has asked you to buy marble tile imported from Italy for her kitchen

floor. The dimensions of her rectangular kitchen are 12’ × 15’. Your grandmother wants

to compare the price of using square tiles versus hexagonal tiles. The length of one side

of a square tile is 6’’ with a cost of $3.50 a piece and the length of one side of a

Tessellations Worksheet Page 3