Use the image to answer the question.

Question

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¯¯¯¯¯¯¯¯≅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¯¯¯¯¯¯¯¯¯¯
Modifying above upper N upper L with bar congruent to Modifying above upper K upper M with bar

KM¯¯¯¯¯¯¯¯¯¯≅KN¯¯¯¯¯¯¯¯¯

Answer 1

To determine that triangles \( \triangle KLM \) and \( \triangle MNK \) are congruent using the SSS (Side-Side-Side) Congruence Theorem, you need to know that all corresponding sides of the triangles are equal in length.

Among the provided options, you would need a relationship confirming another pair of sides to apply the SSS theorem effectively:

• The correct response is: NL¯¯¯¯¯¯¯¯≅KM¯¯¯¯¯¯¯¯¯¯.

This equivalence states that side \( NL \) is congruent to side \( KM \), which, along with the other two pairs of sides that are already known to be congruent, would allow you to conclude the congruence of the two triangles.

Answer 2

Use the image to answer the question.

An illustration shows two congruent triangles in different orientations. Three corresponding sides are marked as congruent.

Are the triangles congruent? If so, write a congruence statement and reason why.

(1 point)
Responses

Yes, △ABC≅△LNM by the SSS Congruence Theorem.
Yes, triangle upper A upper B upper C congruent to triangle upper L upper N upper M by the SSS Congruence Theorem.

Yes, △ABC≅△MLN by the SSS Congruence Theorem.
Yes, triangle upper A upper B upper C congruent to triangle upper M upper L upper N by the SSS Congruence Theorem.

No, the triangles are not congruent.
No, the triangles are not congruent.

Yes, △ABC≅△LMN by the SSS Congruence Theorem.

Answer 3

Yes, the triangles are congruent.

The correct response is: Yes, \( \triangle ABC \cong \triangle LMN \) by the SSS Congruence Theorem.

The congruence of the triangles is established because all three sides of one triangle are marked as congruent to the corresponding sides of the other triangle. According to the SSS (Side-Side-Side) Congruence Theorem, if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.