30. Think About a Plan A semiregular tessellation is made up of two or more different regular polygons, with the same arrangement of the polygons at each vertex. Can you use regular octagons and squares, all with side length 1 unit, to make a semiregular tessellation? If so, draw a sketch.
    • Why is knowing that the figures have the same side length important?
    • What is the sum of the measures of the angles at each vertex?

One hexagon, two squares, and one equilateral triangle meet at each vertex of this semiregular tessellation.

Can you make a semiregular tessellation using the given pair of regular polygons? If so, draw a sketch.

Determine whether each statement is always, sometimes, or never true. Explain.

33. A scalene triangle will tessellate.
34. A rhombus will tessellate.
35. A hexagon will tessellate.
36. A regular decagon will tessellate.

Can each set of polygons be used to make a tessellation? If so, draw a sketch.

List the types of symmetry each tessellation has.

C Challenge

41. Follow these steps to make a tessellation of a quadrilateral.
    1. Draw quadrilateral ABCD with no two sides congruent. Locate M, the midpoint of A B ¯ , eh b bar , comma  and N, the midpoint of B C ¯ . b c bar , .
    2. Draw the image of ABCD for a 180 ° 180 degrees  rotation about M.
    3. Draw the image of ABCD for a 180 ° 180 degrees  rotation about N.
    4. Draw the image of ABCD for the translation that maps D to B.

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