Tessellations Geometry 12 6 Tessellation tiling An arrangement

Tessellations Geometry 12 -6

• Tessellation (tiling) – An arrangement of shapes so that they completely cover a plane without any overlap or gaps • Monohedral Tessellation – A tessellation using only one shape Vocabulary

Which of the following are tessellations? Tessellations

• Regular Tessellation – A monohedral tessellation made up of regular congruent polygons Vocabulary

Tessellations may have more than one type of shape Tessellations

• Vertex Arrangement (numerical name) – A sequence of numbers relating to the sides of the polygons that meet at the vertex in a tiling Vocabulary

Tessellations

Name the vertex arrangement for each arrowed location Tessellations

Tessellation with non regular polygons Tessellations using only translations Tessellations

• Get your supplies – Blank Paper – Scissors Investigation

Investigation

Investigation

• Any triangle will create a monohedral tessellation Conjecture

Investigation

• Any quadrilateral will create a monohedral tessellation Conjecture

Tessellation using only translation

Examples

Examples

• Get your supplies – Blank Paper – Scissors – Tape Investigation

• Create your own rectangle tessellation • Start with a rectangle and then alter it as in the four steps on the next page Investigation

Investigation

• Create your own hexagon tessellation • Start with a hexagon and then alter it as in the six steps on the next page Investigation

Investigation

Investigation

Tessellations that use rotation

• Observe a hexagon tessellation • Start with a hexagon and then alter it as in the six steps on the next page Investigation

Investigation

TRIANGLE TESSELLATIONS

• Supplies – Paper – Scissors – Straightedge Investigation

• Draw a single scalene triangle (about ¼ the size of a sheet of paper) Investigation

• Label the vertices I, F & H F H I Investigation

• Create a design along the line IF, then transfer the design to the line IH as shown Investigation

• Find the midpoint of line FH, label the point S S Investigation

• Create a design between S and H Investigation

• Rotate the design between SH to fit between SF, as shown Investigation

• Trace the design onto paper, and cut out at least six shapes Investigation

Investigation

Tessellations that glide reflections

• Observe a triangle glide refelction tessellation • Start with a triangle and then alter it as in the six steps on the next page Investigation

Investigation

Investigation

• Observe a quadrilateral glide translation tessellation • Start with a quadrilateral and then alter it as in the four steps on the next page Investigation

Investigation

Investigation

• Pages 670 – 672 • 11 – 16, 49 – 50 Homework