If a tile is a square or rectangle, cut the tile from corner to corner and you will create two triangles.
yes
Yes.
No
An [equilateral] triangle, square and hexagon are the only regular polygons which, by themselves, will tile a surface.
Yes.
yes
Yes.
Yes.
Yes a triangle will tessellate leaving no gaps or overlaps
yes it does
No
No.
heptagon and an equilateral triangle
An [equilateral] triangle, square and hexagon are the only regular polygons which, by themselves, will tile a surface.
Yes.
It can, by itself.
Yes, you can stain tile to change its color or appearance by using a specialized tile stain or dye.