The valid names for the triangle are determined by the vertices of the triangle. In this scenario, the vertices are denoted as A, M, D, and K. Therefore, the valid names for the triangle should only contain these vertices.
Let's verify which options are valid:
A. ASKD: This name uses all vertices of the triangle and is therefore valid.
B. AMDK: This name also uses all vertices of the triangle and is consequently valid.
C. ADKM: This name too uses all vertices of the triangle and is thus valid.
D. AKMD: This name is not valid because it includes the vertex 'ᴋ' which is not a vertex of the triangle.
E. ΛKE: This name is not valid because it includes the vertex 'ᴋ' and 'E' which are not vertices of the triangle.
F. ASKMO: This name is not valid because it includes the vertex 'ᴋ' and 'O' which are not vertices of the triangle.
From this analysis, none of the choices are valid names for the triangle.
The important thing to remember here is that when naming a triangle, we must use the vertices that are part of the triangle. Other vertices that are not part of the triangle should not be used in the naming.