Two triangles have side lengths 6, 8, 10 and 9, 12, 15. Are they similar?

• A. No, they are not similar.
• B. Yes, by SSS Similarity.
• C. Yes, by AA Similarity.
• D. Yes, they are congruent.

Answer: (B)

Similarity via proportional sides: if two triangles have corresponding sides in the same ratio, the triangles are similar and their corresponding angles are equal. Here, the first triangle has sides 6, 8, 10 and the second has 9, 12, 15. Each side of the second is 1.5 times the corresponding side of the first (9/6 = 12/8 = 15/10 = 3/2). So all three side lengths are scaled by the same factor, which guarantees similarity. They are not congruent because the side lengths are not equal (the second is larger by a factor of 1.5). Also, both triangles are 3-4-5 triples, hence right triangles, which also aligns with the angle equality, reinforcing the similarity.