import geometry;
import animation;

size(10cm);

line e = line( 45, origin),
     f = line(-45, origin);

pen sidestyle = 2+defaultpen,
    diagonalstyle = longdashed,
    squarestyle = dotted,
    altitudestyle = red+longdashed,
    positivestyle = palered,
    negativestyle = paleblue;

draw(e, diagonalstyle);
draw(f, diagonalstyle);

real alt = 10,
     semialt = alt / 2;
draw(box((-alt, -alt), (alt, alt)), invisible);

animation movingtrapezoid = animation("movingtrapezoid");
animation withsquare = animation("withsquare");
animation hints = animation("hints");

void now(real y)
{	real yUp = y + semialt,
	     yDown = y - semialt;
	point A = ( yDown, yDown),
	      B = (-yDown, yDown),
	      C = ( yUp, yUp),
	      D = (-yUp, yUp);
	point A0 = (-semialt, yDown),
	      B0 = ( semialt, yDown),
	      C0 = ( semialt, yUp),
	      D0 = (-semialt, yUp);
	/*
	segment a = segment(A, B),
	        b = segment(B, C),
	        c = segment(C, D),
	        d = segment(D, A);
	*/
	path a = A--B,
	     b = B--C,
	     c = C--D,
	     d = D--A;
	point FootUp = (0, yUp),
	      FootDown = (0, yDown);
	segment salt = segment(FootDown, FootUp);
	point K1 = (-semialt, y),
	      K2 = ( semialt, y);
	path sq = A0--B0--C0--D0--cycle;
	dot("$A$", A, SW);
	dot("$B$", B, SE);
	dot("$C$", C, NE);
	dot("$D$", D, NW);
	draw(Label("$a$", MidPoint, RightSide), a, sidestyle);
	draw(Label("$b$", MidPoint, RightSide), b, sidestyle);
	draw(Label("$c$", MidPoint, RightSide), c, sidestyle);
	draw(Label("$d$", MidPoint, RightSide), d, sidestyle);
	draw(Label("10", MidPoint, RightSide), salt, altitudestyle, Arrows);
	movingtrapezoid.add();
	draw(sq, squarestyle);
	withsquare.add();
	fill(A--A0--K1--cycle, positivestyle);
	fill(B--B0--K2--cycle, positivestyle);
	fill(C--C0--K2--cycle, negativestyle);
	fill(D--D0--K1--cycle, negativestyle);
	hints.add();
}

real epsilon = 0.1;
for (real y = -semialt + 9epsilon; y < semialt - 9epsilon; y+= epsilon)
{	save();
		now(y);
	restore();
}
movingtrapezoid.movie();
hints.movie();
withsquare.movie();