There are exactly three kinds of irregular, convex hexagons that tile the plane. Conside...

There are exactly three kinds of irregular, convex hexagons that tile the plane. Consider the following hexagon with vertex angles labeled with capital letters and side lengths labeled with lower case letters.

All regular hexagons will tile a plane. For irregular, convex hexagons to tile the plane, any one of the following sets of conditions must hold:

(I) A + B + C = 360°, and f = c

(II) A + C + D = 360°, a = d, and b = f

(III) A = C = E = 120°, a = f, b = c, and e = d

Consider the following convex, irregular hexagon.

a. Which set of conditions I, II, or III does the hexagon satisfy?

b. Copy, cut out, and paste at least six copies of the hexagon on your paper to form a tiling.