Two similar triangles T1 and T2 are triangles whose corresponding angles are congruent and whose corresponding sides are in proportion.

The routine returns true if T1 and T2 are similar; false if they are not; and FAIL if it is unable to reach a conclusion.

In FAIL is returned, and the optional argument is given, the condition that makes T1 and T2 similar is assigned to this argument. It will be either of the form  or of the form  where expr, expr_i are Maple expressions.

The command with(geometry,AreSimilar) allows the use of the abbreviated form of this command.

AreSimilar:   "hint: one of the following conditions must be satisfied: {{9/Hy^2-10/(Gx^2+1) = 0, 9/Hy^2-1/(Gx^2+(Hy-1)^2) = 0}, {9/Hy^2-1/(Gx^2+1) = 0, 9/Hy^2-10/(Gx^2+(Hy-1)^2) = 0}, {9/(Gx^2+1)-10/Hy^2 = 0, 9/(Gx^2+1)-1/(Gx^2+(Hy-1)^2) = 0}, {9/(Gx^2+1)-1/Hy^2 = 0, 9/(Gx^2+1)-10/(Gx^2+(Hy-1)^2) = 0}, {9/(Gx^2+(Hy-1)^2)-10/Hy^2 = 0, 9/(Gx^2+(Hy-1)^2)-1/(Gx^2+1) = 0}, {9/(Gx^2+(Hy-1)^2)-1/Hy^2 = 0, 9/(Gx^2+(Hy-1)^2)-10/(Gx^2+1) = 0}}"