Question

The SSS Congruence Theorem Quick Check 4 of 54 of 5 Items Question Use the image to answer the question. What additional piece of information would you need to be able to state that △KLM≅△MNK by the SSS Congruence Theorem? (1 point) Responses NL¯¯¯¯¯¯¯¯≅KM¯¯¯¯¯¯¯¯¯¯ Modifying above upper N upper L with bar congruent to Modifying above upper K upper M with bar 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 Skip to navigation page 15 of 15 Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.

Answer 1

To determine if triangles \( \triangle KLM \) and \( \triangle MNK \) are congruent using the SSS Congruence Theorem, we need to know that all three sides of one triangle are congruent to the corresponding three sides of the other triangle.

The SSS Congruence Theorem states that if three sides of one triangle are equal in length to three sides of another triangle, then the two triangles are congruent.

Given the options you're considering, you need to find a statement that ensures that the lengths of the sides meet the SSS requirement.

From the options presented, identifying one that states the congruence of an additional side length is what you need:

1. \( \overline{NL} \cong \overline{KM} \) – This provides one side but may not confirm sufficient information.
2. \( \overline{KM} \cong \overline{KN} \) – Again, this gives one side which is not enough.
3. \( \overline{KL} \cong \overline{MN} \) – This indicates a congruence of another side.
4. \( \overline{KL} \cong \overline{LM} \) – Similarly, this confirms congruence between one other side.

For SSS to work, you would need congruence relating all three corresponding sides between \( \triangle KLM \) and \( \triangle MNK \).

Among those pieces of information, the best option is:

• \( \overline{KL} \cong \overline{LM} \)

This additional information would confirm the third side, enabling the use of the SSS Congruence Theorem to state that \( \triangle KLM \cong \triangle MNK \).