Asked by PJ
Are the triangles congruent? If so, write a congruence statement and reason why. (1 point)
Yes, △ABC≅△LNM by the SSS Congruence Theorem.
Yes, △ABC≅△LMN by the SSS Congruence Theorem.
No, the triangles are not congruent.
Yes, △ABC≅△MLN by the SSS Congruence Theorem.
Yes, △ABC≅△LNM by the SSS Congruence Theorem.
Yes, △ABC≅△LMN by the SSS Congruence Theorem.
No, the triangles are not congruent.
Yes, △ABC≅△MLN by the SSS Congruence Theorem.
Answers
Answered by
GPT-4o mini
To determine if the triangles are congruent, we need to consider the SSS (Side-Side-Side) Congruence Theorem, which states that if three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.
Based on the options provided, we see two variations:
1. **Yes, △ABC≅△LNM by the SSS Congruence Theorem.**
2. **Yes, △ABC≅△LMN by the SSS Congruence Theorem.**
3. **No, the triangles are not congruent.**
4. **Yes, △ABC≅△MLN by the SSS Congruence Theorem.**
The key to determining the correct answer is the orientation and the naming of the triangles. The important aspects are as follows:
- The order of the corresponding vertices should match based on the sides provided for comparison.
- If two triangles have sides that are equal in length, regardless of the orientation, they are congruent.
If the sides of triangles ABC and LNM (or LMN or MLN) are known to be equal in the same configuration, any statement indicating they are congruent by the SSS Theorem is valid.
However, if the sides are not mentioned or if you believe the triangles named do not have equal sides, the correct answer would be **No, the triangles are not congruent.**
Assuming sides are equal and depending on the order of naming, the most accurate option would be one of the first three options, where the triangle names seem to compare same side lengths.
To finalize, if you have specific side lengths or values indicating they are equal, you should select the appropriate congruence statement that fits those dimensions. But without this information, we can only confirm potential congruency based on the SSS theorem and the naming order.
If the sides match, choose one of the first three 'Yes' options based on the correct naming convention. If not sure, go with **No, the triangles are not congruent.**
Based on the options provided, we see two variations:
1. **Yes, △ABC≅△LNM by the SSS Congruence Theorem.**
2. **Yes, △ABC≅△LMN by the SSS Congruence Theorem.**
3. **No, the triangles are not congruent.**
4. **Yes, △ABC≅△MLN by the SSS Congruence Theorem.**
The key to determining the correct answer is the orientation and the naming of the triangles. The important aspects are as follows:
- The order of the corresponding vertices should match based on the sides provided for comparison.
- If two triangles have sides that are equal in length, regardless of the orientation, they are congruent.
If the sides of triangles ABC and LNM (or LMN or MLN) are known to be equal in the same configuration, any statement indicating they are congruent by the SSS Theorem is valid.
However, if the sides are not mentioned or if you believe the triangles named do not have equal sides, the correct answer would be **No, the triangles are not congruent.**
Assuming sides are equal and depending on the order of naming, the most accurate option would be one of the first three options, where the triangle names seem to compare same side lengths.
To finalize, if you have specific side lengths or values indicating they are equal, you should select the appropriate congruence statement that fits those dimensions. But without this information, we can only confirm potential congruency based on the SSS theorem and the naming order.
If the sides match, choose one of the first three 'Yes' options based on the correct naming convention. If not sure, go with **No, the triangles are not congruent.**