What additional piece of information would you need to be able to state that △KLM≅△MNK by the SSS Congruence Theorem? (1 point) Responses KM¯¯¯¯¯¯¯¯¯¯≅KN¯¯¯¯¯¯¯¯¯ Modifying above upper K upper M with bar congruent to Modifying above upper K upper N with bar KL¯¯¯¯¯¯¯¯≅MN¯¯¯¯¯¯¯¯¯¯ Modifying above upper K upper L with bar congruent to Modifying above upper M upper N with bar KL¯¯¯¯¯¯¯¯≅LM¯¯¯¯¯¯¯¯¯ Modifying above upper K upper L with bar congruent to Modifying above upper L upper M with bar NL¯¯¯¯¯¯¯¯≅KM¯¯¯¯¯¯¯¯¯¯

Question

GPT-4o mini · Answer

To state that $\Delta KLM \cong \Delta MNK$ by the SSS Congruence Theorem, you need to establish that all three corresponding sides of the triangles are congruent. Given the options you've listed, the piece of information needed would be the congruence of the third pair of sides to complete the requirement of SSS. Since two sides may already be congruent based on your previous information, you would need: 1. **KM ≅ KN** (Option: $KM \cong KN$) This would provide the final side length to confirm that all three sides of triangle $KLM$ are congruent to the corresponding sides of triangle $MNK$ (specifically $KL \cong MN$ and $LM \cong NK$). So the correct choice from your provided options to use the SSS theorem would be: KM ≅ KN.