Question
What additional piece of information would you need to be able to state that \(\triangle
KLM\cong\triangle MNK\) by the SSS Congruence Theorem?
(1 point)
\(\overline{KL}\cong\overline{LM}\)
\(\overline{KL}\cong\overline{MN}\)
\(\overline{KM}\cong\overline{KN}\)
\(\overline{NL}\cong\overline{KM}\)
KLM\cong\triangle MNK\) by the SSS Congruence Theorem?
(1 point)
\(\overline{KL}\cong\overline{LM}\)
\(\overline{KL}\cong\overline{MN}\)
\(\overline{KM}\cong\overline{KN}\)
\(\overline{NL}\cong\overline{KM}\)
Answers
GPT-4o mini
To apply the SSS (Side-Side-Side) Congruence Theorem, you need to establish that all three sides of one triangle are congruent to the three sides of the other triangle.
In this case, we are looking at triangles \(\triangle KLM\) and \(\triangle MNK\). For these two triangles to be congruent by SSS, we need the following correspondences to hold:
1. One side of triangle \(\triangle KLM\) must be congruent to one side of triangle \(\triangle MNK\),
2. Another side of triangle \(\triangle KLM\) must be congruent to the corresponding side of triangle \(\triangle MNK\),
3. The remaining side must also be congruent.
From the statements given:
1. \(\overline{KL} \cong \overline{LM}\): This compares two sides of \(\triangle KLM\) but does not help in establishing congruence with \(\triangle MNK\).
2. \(\overline{KL} \cong \overline{MN}\): This provides one side congruence between the triangles.
3. \(\overline{KM} \cong \overline{KN}\): This does not directly relate to sides of \(\triangle KLM\).
4. \(\overline{NL} \cong \overline{KM}\): This compares one side of \(\triangle KLM\) with one of \(\triangle MNK\), but does not complete all side comparisons.
The critical piece we are missing is a second comparison for the sides, which completes the mapping for all three sides necessary for SSS congruence. Since \(\overline{KL} \cong \overline{MN}\) provides us one side congruence, we would also need another corresponding side equivalency.
Based on the options, the best choice to establish necessary side congruence would therefore be:
**Answer: \(\overline{KL} \cong \overline{MN}\)**
However, without further information showing another congruence between sides, it wouldn't be enough to determine if the triangles are congruent via SSS. You would need the information confirming another side – perhaps from the choices provided you’d choose \(\overline{NL} \cong \overline{KM}\), but this is not as directly a part of a typical SSS statement and thus would require context to be fully effective.
A more direct answer would likely be necessary based on what would establish the essential conditions for SSS.
In this case, we are looking at triangles \(\triangle KLM\) and \(\triangle MNK\). For these two triangles to be congruent by SSS, we need the following correspondences to hold:
1. One side of triangle \(\triangle KLM\) must be congruent to one side of triangle \(\triangle MNK\),
2. Another side of triangle \(\triangle KLM\) must be congruent to the corresponding side of triangle \(\triangle MNK\),
3. The remaining side must also be congruent.
From the statements given:
1. \(\overline{KL} \cong \overline{LM}\): This compares two sides of \(\triangle KLM\) but does not help in establishing congruence with \(\triangle MNK\).
2. \(\overline{KL} \cong \overline{MN}\): This provides one side congruence between the triangles.
3. \(\overline{KM} \cong \overline{KN}\): This does not directly relate to sides of \(\triangle KLM\).
4. \(\overline{NL} \cong \overline{KM}\): This compares one side of \(\triangle KLM\) with one of \(\triangle MNK\), but does not complete all side comparisons.
The critical piece we are missing is a second comparison for the sides, which completes the mapping for all three sides necessary for SSS congruence. Since \(\overline{KL} \cong \overline{MN}\) provides us one side congruence, we would also need another corresponding side equivalency.
Based on the options, the best choice to establish necessary side congruence would therefore be:
**Answer: \(\overline{KL} \cong \overline{MN}\)**
However, without further information showing another congruence between sides, it wouldn't be enough to determine if the triangles are congruent via SSS. You would need the information confirming another side – perhaps from the choices provided you’d choose \(\overline{NL} \cong \overline{KM}\), but this is not as directly a part of a typical SSS statement and thus would require context to be fully effective.
A more direct answer would likely be necessary based on what would establish the essential conditions for SSS.