The leg-leg theorem cannot be used to prove that triangle ABC is congruent to triangle DEC because the leg-leg theorem only applies to right triangles.
The leg-leg theorem states that if two right triangles have two congruent legs, then the triangles are congruent. The given image shows two triangles, ABC and DEC, but we do not have enough information to determine if their legs are congruent.
The given information does not state that triangle ABC and triangle DEC are right triangles, so we cannot use the leg-leg theorem to prove their congruence.
Instead, we need to use other congruence postulates such as side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), or angle-angle-side (AAS) to prove the congruence of the two triangles.
To use the leg-leg theorem, we would need to know that either AB = DE or AC = EC.
Therefore, we cannot use the leg-leg theorem to prove that triangle ABC is congruent to triangle DEC.