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Pre-Algebra

Learn to predict and verify patterns involving tessellations. 5-9. Tessellations. Pre-Algebra. 5-9. Tessellations. Pre-Algebra. Fascinating designs can be made by repeating a figure or group of figures. These designs are often used in art and architecture.

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Pre-Algebra

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  1. Learn to predict and verify patterns involving tessellations. 5-9 Tessellations Pre-Algebra

  2. 5-9 Tessellations Pre-Algebra Fascinating designs can be made by repeating a figure or group of figures. These designs are often used in art and architecture. A repeating pattern of plane figures that completely covers a plane with no gaps or overlaps is a tessellation.

  3. 5-9 Tessellations Pre-Algebra In a regular tessellation, a regular polygon is repeated to fill a plane. The angles at each vertex add to 360°,so exactly three regular tessellations exist.

  4. 5-9 Tessellations Pre-Algebra In a semiregular tessellation, two or more regular polygons are repeated to fill the plane and the vertices are all identical.

  5. 1 5-9 Tessellations Understand the Problem Pre-Algebra Additional Example 1: Problem Solving Application Find all the possible semiregular tessellations that use triangles and squares. List the important information: • The angles at each vertex add to 360°. • All the angles in a square measure 90°. • All the angles in an equilateral triangle measure 60°.

  6. 2 5-9 Make a Plan Tessellations Pre-Algebra Additional Example 1 Continued Account for all possibilities: List all possible combinations of triangles and squares around a vertex that add to 360°. Then see which combinations can be used to create a semiregular tessellation. 6 triangles, 0 squares 6(60°) = 360° regular 3 triangles, 2 squares 3(60°) + 2(90°) = 360° 0 triangles, 4 squares 4(90°) = 360° regular

  7. 5-9 Tessellations 3 Solve Pre-Algebra Additional Example 1 Continued There are two arrangements of three triangles and two squares around a vertex.

  8. 5-9 Tessellations 3 Solve Pre-Algebra Additional Example 1 Continued Repeat each arrangement around every vertex, if possible, to create a tessellation.

  9. 5-9 Tessellations 3 Solve Pre-Algebra Additional Example 1 Continued There are exactly two semiregular tessellations that use triangles and squares.

  10. 5-9 Tessellations 4 Look Back Pre-Algebra Additional Example 1 Continued Every vertex in each arrangement is identical to the other vertices in that arrangement, so these are the only arrangements that produce semiregular tessellations.

  11. 5-9 Tessellations Pre-Algebra Additional Example 2: Creating a Tessellation Create a tessellation with quadrilateral EFGH. There must be a copy of each angle of quadrilateral EFGH at every vertex.

  12. I J K L 5-9 Tessellations Pre-Algebra Try This: Example 2 Create a tessellation with quadrilateral IJKL. There must be a copy of each angle of quadrilateral IJKL at every vertex.

  13. 5-9 Tessellations Pre-Algebra Try This: Example 3 Use rotations to create a tessellation with the quadrilateral given below. Step 1: Find the midpoint of a side. Step 2: Make a new edge for half of the side. Step 3: Rotate the new edge around the midpoint to form the edge of the other half of the side. Step 4: Repeat with the other sides.

  14. 5-9 Tessellations Pre-Algebra Try This: Example 3 Continued Step 5: Use the figure to make a tessellation.

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