AMC 12 2003b Problem 10

Several figures can be made by attaching two equilateral triangles to the regular pentagon ABCDE in two of the five positions shown. How many non-congruent figures can be constructed in this way?

size(200);
defaultpen(0.9);
real r = 5/dir(54).x, h = 5 tan(54*pi/180);
pair A = (5,0), B = A+10*dir(72), C = (0,r+h), E = (-5,0), D = E+10*dir(108);
draw(A--B--C--D--E--cycle);
label("$A$",A+(0,-0.5),SSE);
label("$B$",B+(0.5,0),ENE);
label("$C$",C+(0,0.5),N);
label("$D$",D+(-0.5,0),WNW);
label("$E$",E+(0,-0.5),SW);
//
real l = 5*sqrt(3); pair ab = (h+l)*dir(72), bc = (h+l)*dir(54);
pair AB = (ab.y, h-ab.x), BC = (bc.x,h+bc.y), CD = (-bc.x,h+bc.y), DE = (-ab.y, h-ab.x), EA = (0,-l);
draw(A--AB--B^^B--BC--C^^C--CD--D^^D--DE--E^^E--EA--A, dashed);
//
dot(A); dot(B); dot(C); dot(D); dot(E); dot(AB); dot(BC); dot(CD); dot(DE); dot(EA);

$\text {(A) } 1 \text {(B) } 2 \text {(C) } 3 \text {(D) } 4 \text {(E) } 5$