An illustration shows a horizontal parallelogram divided into two triangles.
What additional piece of information would you need to be able to state that △KLM≅△MNK by the SSS Congruence Theorem?
(1 point)
Responses
KL¯¯¯¯¯¯¯¯≅LM¯¯¯¯¯¯¯¯¯
Modifying above upper K upper L with bar congruent to Modifying above upper L upper M with bar
KM¯¯¯¯¯¯¯¯¯¯≅KN¯¯¯¯¯¯¯¯¯
Modifying above upper K upper M with bar congruent to Modifying above upper K upper N with bar
NL¯¯¯¯¯¯¯¯≅KM¯¯¯¯¯¯¯¯¯¯
Modifying above upper N upper L with bar congruent to Modifying above upper K upper M with bar
KL¯¯¯¯¯¯¯¯≅MN¯¯¯¯¯¯¯¯¯¯
Modifying above upper K upper L with bar congruent to Modifying above upper M upper N with bar
The additional piece of information needed would be: KL¯¯¯¯¯¯¯¯≅MN¯¯¯¯¯¯¯¯¯¯
To be able to state that ΔKLM ≅ ΔMNK by the SSS Congruence Theorem, we would need the additional piece of information that KL ≅ MN.
To determine if triangles △KLM and △MNK are congruent using the SSS Congruence Theorem, we need to ensure that all corresponding sides of the triangles are congruent.
From the given information, we are told that KL¯¯¯¯¯¯¯¯≅LM¯¯¯¯¯¯¯¯¯ (side KL is congruent to side LM). However, this alone is not sufficient to apply the SSS Congruence Theorem.
To establish congruence using the SSS Congruence Theorem, we would need another pair of corresponding sides to be congruent. From the options provided, we can see that one of the statements is KL¯¯¯¯¯¯¯¯≅MN¯¯¯¯¯¯¯¯¯¯ (side KL is congruent to side MN). Therefore, if we have this additional piece of information, we would be able to state that △KLM≅△MNK by the SSS Congruence Theorem.