Q:

• • • • Choose one kind of triangle to use for a tessellation: equilateral, isosceles, or scalene. Use technology or paper to create six or more congruent copies of your chosen triangle and investigate how the shape tessellates. Use your chosen triangle to create an artwork with tessellations. You can use any sizes, colors, patterns, or art mediums. You can submit a scanned copy, photo, screenshot, or snip of your artwork. Provide the explanation of the math behind your tessellation that the gallery will display next to your artwork. oo oUse the definition of your chosen triangle and what you know about the interior angles of triangles to prove that any version or size of that triangle will tessellate. (Hint: Study the interior angles where the vertices meet in the tessellation.) Include diagrams or other visual models to help explain your proof. Think about how you could extend your work to prove that all triangles tessellate, and share any theories you might have

Accepted Solution

A:
Tessellation is the arrangement of congruent shapes, with no gaps and overlaps. The tessellation artwork (Picture 1) used equilateral triangles, distinguished by two designs.

An equilateral triangle has equal angles which measures 60 degrees. Hence, in this tessellation, the vertex (point where the triangles meet), total angle is 360 degrees. See picture 2 for proof.