1. what is a tessellation, and how are transformations used to create a tessellation?2. which regular polygons tessellate? (list all.) 3. consider your answer to question 2. why do these regular polygons tessellate while other regular polygons do not? include a discussion of interior angles in your response. also include an example of a regular polygon that would not tessellate and explain why it would not. 4. using your geometry software, create a regular tessellation. you may use color patterns to make the tessellation more visually interesting. make a screenshot of your tessellation and paste it into this assignment. in the space provided below, write a detailed explanation of the steps you followed to create your tessellation. a model worksheet and response have been provided for you. if you choose to tessellate the same regular polygon as the example provided, you must use different transformations from those used in the model.

1. Tessellation is the covering of a surface with a pattern of flat shapes so that there are no overlaps or gaps. It is also called Tiling.

2. Triangles, Squares, and Hexagons.

3. Previous three shapes create a regular tessellation pattern because all their sides and all their angles are the same. the intersection point of the interior angles is called "Vertex". For a regular tessellation, the pattern is identical at each Vertex.

Unlike the triangle and quadrilateral case, the Pentagon's angle sum of 540° is not helpful when trying to fit a bunch of Pentagons around a vertex. Therefore, even though the Pentagon is a regular polygon, it cannot tessellate.

4. See attached screenshot of 3 tessellations created with Tessellation Artist Software online.

use formula for the circle a=3.14

step-by-step explanation:

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation: