TESSELLATIONS Oleh : Sulistyana SMP N 1 Wonosari

What kind of a geometrical shape forms this design?

INDICATORS: Creating tessellations using equilateral triangle, regular hexagon, rhombus, and trapezoid. Explaining whether tessellation can be created using a square and an equilateral triangle, and justifying the answer with a figure. Determining the sum of measures of the angles where the vertices of the figures meet in the tessellations. Determining the name of two figures that cannot be used to create a tessellation and justifying the answer with a figure. Creating tessellation using other pattern blocks.

Tessellations A pattern formmed by repeating figures that fit together without gaps or overlaps is a tessellation. Tessellations are formed using translation(slides), reflection(flips), or rotation(turns) of congruent figures

Three Common Transformations 1. Translation, which is a slide of one side of the polygon. 2. Reflection, which is a flip or mirror image of one side of the polygon. Read slide… There are other transformations … really combinations of these three… click when completed... 3. Rotation, which is a turn of a side around one vertex of the polygon.

Reflections

Reflections

Tessellation from a rotation Have students complete using third space on worksheet… Use pen tool to model…. click when completed...

Let’s try together a rotation Have students complete using third space on worksheet… Use pen tool to model…. click when completed...

Tessellation Have students complete using third space on worksheet… A pattern of shapes that fit perfectly together! A Tessellation (or Tiling) is when you cover a surface with a pattern of flat shapes so that there are no overlaps or gaps. Have students complete using third space on worksheet… Use pen tool to model…. click when completed... Examples: Rectangles Octagons and Squares Different Pentagons

1. Regular Tessellations A regular tessellation is a pattern made by repeating a regular polygon. Have students complete using third space on worksheet… Use pen tool to model…. click when completed... Triangles 3.3.3.3.3.3 Squares 4.4.4.4 Hexagons 6.6.6 There are only 3 regular tessellations

Look at a Vertex ... Have students complete using third space on worksheet… Use pen tool to model…. click when completed...

2. Semi-regular Tessellations A semi-regular tessellation is made of two or more regular polygons. The pattern at each vertex must be the same! Have students complete using third space on worksheet… Use pen tool to model…. click when completed... There are only 8 semi-regular tessellations:

3. Other Tessellations There are also "demiregular" tessellations, but mathematicians disagree on what they actually are! And some people allow curved shapes (not just polygons) so you can have tessellations like these: Have students complete using third space on worksheet… Use pen tool to model…. click when completed...

Have students complete using third space on worksheet… Use pen tool to model…. click when completed...

Have students complete using third space on worksheet… Use pen tool to model…. click when completed...

Have students complete using third space on worksheet… Use pen tool to model…. click when completed...

Have students complete using third space on worksheet… Use pen tool to model…. click when completed...