If triangles ABC and DEF are similar with AB corresponding to DE and AC to DF, and AB = 8, DE = 4, AC = 10, DF = 5, what is the similarity scale factor from DEF to ABC?

If triangles ABC and DEF are similar with AB corresponding to DE and AC to DF, and AB = 8, DE = 4, AC = 10, DF = 5, what is the similarity scale factor from DEF to ABC?

• A. 1
• B. 2
• C. 0.5
• D. 4

Answer: (B)

Similar triangles have a constant ratio between corresponding side lengths. To go from triangle DEF to triangle ABC, use the pairs DE with AB and DF with AC. If the scale factor is k, then DE × k = AB and DF × k = AC. So k = AB/DE = 8/4 = 2, and k = AC/DF = 10/5 = 2. Both pairs give the same value, confirming the factor. Therefore, the similarity scale factor from DEF to ABC is 2, meaning ABC is twice as large as DEF.

Similar triangles have a constant ratio between corresponding side lengths. To go from triangle DEF to triangle ABC, use the pairs DE with AB and DF with AC. If the scale factor is k, then DE × k = AB and DF × k = AC. So k = AB/DE = 8/4 = 2, and k = AC/DF = 10/5 = 2. Both pairs give the same value, confirming the factor. Therefore, the similarity scale factor from DEF to ABC is 2, meaning ABC is twice as large as DEF.