Gary is using a combination of regular polygonal tiles for his kitchen floor. He begins the tessellation at a vertex by placing one square and two triangles.

Which two polygons should he use to fill up the vacant space at the vertex and make it possible to tessellate the floor?

2 hexagons because 360 – (120 + 60 +60) = 120

2 squares because 180 = 90 + 90

1 triangle and 1 hexagon because 180 = 60 + 120

1 square and 1 triangle because 360 – (90 + 60 + 60) = 90 + 60

Question

Gary is using a combination of regular polygonal tiles for his kitchen floor. He begins the tessellation at a vertex by placing one square and two triangles. 
  
Which two polygons should he use to fill up the vacant space at the vertex and make it possible to tessellate the floor?

 2 hexagons because 360 – (120 + 60 +60) = 120

 2 squares because 180 = 90 + 90

 1 triangle and 1 hexagon because 180 = 60 + 120

 1 square and 1 triangle because 360 – (90 + 60 + 60) = 90 + 60

ivettef365 · Answer

He began by using 1 square and 2 triangles, therefore to tessellate it needs one more triangle, so 1 triangle and a square will definitely tessellate

anonymous · Answer

wait @ivettef365, i don't understand. why does it need one more triangle to tesselate?

ivettef365 · Answer

ok, imagine you have two triangles and you put them together, it needs a perfect, you have a whole in the middle that fits a triangle perfectly