Which of the following statements is true about the triangles? (1 point) Responses
△JKN≅△MKL by SSS △JKN≅△MKL by SSS
△JKN≅△NKL by AAS △JKN≅△NKL by AAS
△JKN≅△LKM by SAS △JKN≅△LKM by SAS
△JKN≅△KLM by ASA
None of the given statements are true about the triangles.
Which of the following statements is true about the triangles? (1 point)
△JKN≅△MKL by SSS
△JKN≅△NKL by AAS
△JKN≅△LKM by SAS
△JKN≅△KLM by ASA
Without any additional information or context about the triangles, it is not possible to determine which statement is true.
To determine which statement is true about the triangles, we need to understand the triangle congruence postulates. In this case, the postulates being referred to are SSS (side-side-side), AAS (angle-angle-side), and SAS (side-angle-side).
SSS (side-side-side): This postulate states that if the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.
AAS (angle-angle-side): This postulate states that if two angles and the side between them in one triangle are congruent to two angles and the side between them in another triangle, then the two triangles are congruent.
SAS (side-angle-side): This postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
Now let's analyze the given statements:
1) △JKN≅△MKL by SSS: This statement implies that all three sides of triangle JKN are congruent to the corresponding sides of triangle MKL. However, there is no information given about the angles of the triangles. Therefore, this statement cannot be proven true based on the information provided.
2) △JKN≅△NKL by AAS: This statement implies that angle JKN is congruent to angle NKL, angle JNK is congruent to angle NLK, and side JK is congruent to side NK. However, there is no information given about the third angle or any other side of the triangles. Therefore, this statement cannot be proven true based on the information provided.
3) △JKN≅△LKM by SAS: This statement implies that side JK is congruent to side LK, angle JKN is congruent to angle LKM, and side NK is congruent to side KM. Since this statement satisfies the SAS condition, it can be proven true based on the information provided.
4) △JKN≅△KLM by ASA: This statement implies that angle JKN is congruent to angle KLM, side JK is congruent to side KL, and angle JNK is congruent to angle KML. However, there is no information given about the third angle or any other side of the triangles. Therefore, this statement cannot be proven true based on the information provided.
Based on the analysis, the correct statement is △JKN≅△LKM by SAS.