To prove that two triangles are similar, you can use one of the following statements:
AA (Angle-Angle) Similarity: If two triangles have two pairs of corresponding angles that are congruent, then the triangles are similar.
SAS (Side-Angle-Side) Similarity: If two triangles have two pairs of corresponding sides that are proportional and the included angles are congruent, then the triangles are similar.
SSS (Side-Side-Side) Similarity: If two triangles have all three pairs of corresponding sides that are proportional, then the triangles are similar.
HL (Hypotenuse-Leg) Similarity: If the hypotenuse and one leg of one right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the triangles are similar.
The statement "ΔLKM is similar to ΔNOM because they have the same shape" is not one of the above statements, and therefore cannot be used to prove that the triangles are similar.