History of Tessellation tessellate (verb), tessellation (noun): from Latin tessera "a square tablet" or "a die used for gambling." Latin tessera may have been borrowed from Greek tessares, meaning "four," since a square tile has four sides.
Now continue to paste and position and see if you can tessellate it. Hold down on one of the images and copy it to the clipboard. If you try tiling the plane with these units of tessellation you will find that they cannot be extended infinitely. ConfidentialĮxamples of semi-regular tessellations Confidential The arrangement of polygons at every vertex point is identical. A semiregular tessellation has two properties which are: You can also use a variety of regular polygons to make semi-regular tessellations. A tessellation of triangles has six polygons surrounding a vertex, and each of them has three sides: "3.3.3.3.3.3". For a tessellation of regular congruent hexagons, if you choose a vertex and count the sides of the polygons that touch it, you'll see that there are three polygons and each has six sides, so this tessellation is called "6.6.6": Confidential. Here's how: choose a vertex, and then look at one of the polygons that touches that vertex. A tessellation of squares is named "4.4.4.4". There are four polygons, and each has four sides. For all the others, the interior angles are not exact divisors of 360 degrees, and therefore those figures cannot tile the plane. This works for the triangle, square, and hexagon, and you can show working tessellations for these figures. The regular polygons in a tessellation must fill the plane at each vertex, the interior angle must be an exact divisor of 360 degrees. Interior Measure of angles for the Polygon Confidential a tessellation of hexagons Confidential. We can't show the entire plane, but imagine that these are pieces taken from planes that have been tiled Confidential. Only three regular polygons tessellate in the Euclidean plane:. Remember:Regular means that the sides of the polygon are all the same length Congruent means that the polygons that you put together are all the same size and shape. The word "tessellate" is derived from the Ionic version of the Greek word "tesseres," which in English means "four." ConfidentialĪ regular tessellation means a tessellation made up of congruent regular polygons. A dictionary* will tell you that the word "tessellate" means to form or arrange small squares in a checkered or mosaic pattern. 
Another word for a tessellation is tiling.Lets get startedTessellation A tessellation is created when a shape is repeated over and over again covering a plane without any gaps or overlaps.
Sum of angles in a Quadrilateral = 360 degrees Confidential Square – It is a special case of a rectangle as it has four right angles and parallel sides.Rectangle - A parallelogram in which all angles are right angles.Parallelogram - Quadrilaterals are called parallelograms if both pairs of opposite sides are equal and parallel to each other.Rhombus - A quadrilateral with four equal sides and opposite angles equal.Trapezoid - a quadrilateral with two parallel sides.Right-angled Triangle Sum of angles in a triangle = 180 degrees Confidential.Types of Triangles:Triangles can be classified according to the length of their sides and the size of their angles. Lets review what we have learned In the last Lesson Triangle:Three sided polygon. Find the third angle 60 degrees Confidential The angles of a triangle measure 30 and 90 degrees.Classify the triangle by its sides Isosceles Triangles Three sides of a triangle measure 5, 8, 8 inches.Which quadrilateral has four right angles? Squares and Rectangles.A parallelogram with four equal sides is called a Rhombus.
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