Rotate and Tessellate

Use all geometric shapes below in order to recreate the cat shown. You can translate the shapes by dragging the blue points. To rotate the shapes, drag the green points with the mouse. Click the little icon in the upper right corner in order to reset the worksheet and start over.

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To Find the Measure of the Angles in a Polygon.

Interact with the applet below and answer the questions that follow.

(1). How many copies of the equilateral triangle can you fit together around a single vertex, so that the triangles’ edges have no gaps or overlaps?

(2). What is the measure of each angle in these triangles?

(3). What are the measures of the angles in the square?

(4). What are the measures of the angles in the hexagon?

(5). What are the measures of the angles in the parallelogram?

(6). What are the measures of the right triangle?

(7). What are the measures of the octagon?

(8). What are the measures of the pentagon?

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Design your own Tessellation. 

You will need to decide which shapes you want to use and make copies. Remember that a tessellation is a repeating pattern that goes on forever to fill up the entire plane.

Check the box in the applet below and make your own picture.

(1). Describe a transformation of the picture you created that takes the pattern to itself.

(2). How many different transformations can you find that take the pattern to itself? Consider translations, reflections, and rotations.

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Use the applet below to make a design with rotational symmetry.

Find a transformation that takes the design to itself. Consider rotations, reflections, and translations.