Which of the following statements is true about the triangles below?
A JKN = mkl by sss
B JKN = nkj by aas
C JKN = klm asa
D JKN = lkm by sas
None of the statements is true.
Based on the given information, we can determine that none of the statements A, B, C, or D can be true about the triangles below.
A - SSS (Side-Side-Side) congruence states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. However, no information is given about the lengths of the sides of the triangles, so we cannot determine if they are congruent or not.
B - AAS (Angle-Angle-Side) congruence states that if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the triangles are congruent. Again, no information is given about the angles or sides of the triangles, so we cannot determine if they are congruent or not.
C - ASA (Angle-Side-Angle) congruence states that if two angles and the included side of one triangle are congruent to two angles and the corresponding included side of another triangle, then the triangles are congruent. However, no information is provided about any angles or sides of the triangles, so we cannot determine if they are congruent or not.
D - SAS (Side-Angle-Side) congruence 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 triangles are congruent. Similar to the previous statements, no information is given about the sides or angles of the triangles, so we cannot determine if they are congruent or not.
Therefore, none of the given statements A, B, C, or D can be determined to be true about the triangles below without additional information.
To determine which statement is true about the triangles, we need to understand the meaning of the abbreviations used in the answer choices:
- SSS: Side-Side-Side similarity. It means that all corresponding sides of two triangles are in proportion.
- AAS: Angle-Angle-Side similarity. It means that two corresponding angles and a non-included side of two triangles are congruent.
- ASA: Angle-Side-Angle similarity. It means that two corresponding angles and an included side of two triangles are congruent.
- SAS: Side-Angle-Side similarity. It means that two corresponding sides and the included angle of two triangles are in proportion.
Now, let's analyze each option to see which one follows the given criteria:
A) JKN = mkl by SSS similarity:
This statement compares the sides of triangles JKN and MKL to determine if they are in proportion. However, the given information does not tell us any specific proportions or ratios of the sides. Therefore, we cannot conclude that this statement is true.
B) JKN = nkj by AAS similarity:
This statement compares the angles and side between triangles JKN and NKJ. It states that two angles are congruent, but it does not specify the congruent side. Without this information, we cannot conclude that this statement is true.
C) JKN = klm by ASA similarity:
This statement compares the angles and sides of triangles JKN and KLM. It states that two angles are congruent, and the included side is the third side of both triangles. This satisfies the criteria for ASA similarity. Therefore, this statement could be true, and it is a possible answer.
D) JKN = lkm by SAS similarity:
This statement compares the sides and angle between triangles JKN and LKM. However, the given information does not specify that the included angle is congruent. Without this information, we cannot conclude that this statement is true.
Based on the analysis above, the true statement about the triangles is option C) JKN = klm by ASA.