Defining Tessellations & Concepts

A tessellation is an image created by repeating shapes that cover a plane and have no gaps or overlaps. This means that the shapes fit together perfectly, like puzzle pieces, without leaving any spaces in between or overlapping each other. This concept is often used in art and design to create interesting patterns and designs.

A regular tessellation is a pattern made up of congruent regular polygons that completely covers a plane without any gaps or overlaps. Each polygon must have the same shape and size, and they must fit together perfectly to form a repeating pattern. This ensures that the tessellation is regular and symmetrical. The other options mentioned, such as being composed of normal colors, having angles that all measure 20 degrees, or including a four-sided polygon, are not requirements for a regular tessellation.

The word "vertex" in relation to polygons refers to the point where the lines of the polygons meet. In other words, it is the point where two or more sides of the polygon intersect.

To say that a group of polygons are congruent means that they are all the exact same size and shape. This means that all corresponding sides and angles of the polygons are equal. Congruent polygons can be different from other shapes pictured, but the key characteristic is that they have identical dimensions and shape. The statement about the sides being between 3'' and 8'' in length is not accurate, as congruence is not determined by a specific range of side lengths. The statement about there being 6 or more polygons in the group is also unrelated to the concept of congruence.

The answer is triangles, squares, hexagons. Regular polygons are shapes with equal sides and angles. In a tessellation, these regular polygons fit together perfectly without any gaps or overlaps to cover a plane. Triangles, squares, and hexagons are examples of regular polygons that can tessellate in the Euclidean plane.

A hexagon is a polygon with six sides. To find the angle measure of each angle in a regular hexagon, we can use the formula: (n-2) * 180 / n, where n is the number of sides. Plugging in the value for a hexagon, we get (6-2) * 180 / 6 = 4 * 180 / 6 = 720 / 6 = 120 degrees. Therefore, the angle measure of a hexagon is 120 degrees.

The angle measure of degrees for a triangle is always 180 degrees. In a triangle, the sum of all three angles is always equal to 180 degrees. Therefore, each angle in a triangle is less than 180 degrees. Among the given options, the only angle measure that is less than 180 degrees is 60 degrees.

The question asks for the number of possible semi-regular tessellation combinations. The answer is 8, indicating that there are 8 different combinations possible.