To use the SSS (Side-Side-Side) Congruence Theorem to state that triangle \( \triangle KLM \) is congruent to triangle \( \triangle MNK \), we need to establish that all three pairs of corresponding sides of the triangles are congruent.
Given the options you've provided, for the SSS theorem to hold, we would need information about one of the pairs of sides that has not yet been confirmed as congruent. Here is a breakdown of the options in relation to the requirement:
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\( NL \cong KM \): This option compares side lengths from different triangles, which does not help establish correspondence in all sides.
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\( KL \cong MN \): This option compares another pair of sides, which could help, but we still need information on the third side.
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\( KM \cong KN \): Even though this tries to establish congruence between sides, it still does not cover the needed third corresponding pair.
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\( KL \cong LM \): Again, this pairs sides randomly and does not aid in forming a SSS congruence statement.
In conclusion, to definitively state \( \triangle KLM \cong \triangle MNK \) by the SSS Congruence Theorem, you would need any one of the following pieces of information:
- You would need to know that another specific pair of sides are congruent, such as \( KL \cong MN \), \( KM \cong KN \), or \( LM \cong LN \), as only knowing two pairs will not satisfy the SSS condition.
Thus, the additional specific pair of side (not mentioned previously) must be congruent to establish the SSS congruence.
If we look at your provided options carefully, the best option to answer the question is:
- \( KL \cong MN \)
However, if you only need to select one from your list, I would suggest confirming the validity of any additional side congruences as necessary.