Asked by Makayla
ABC ~ △DEF Which of the following statements is not true? a/c = 2, m∠ D = 80°, 3/c = 6/a, BC ≅ DE
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Answer: BC ≅ DE is not true.
Reason: ABC ~ DEF means A↔D, B↔E, C↔F. So corresponding sides are AB↔DE, BC↔EF, AC↔DF. Thus BC corresponds to EF, not DE, so BC cannot be congruent to DE (unless the scale factor happened to be 1).
Also note 3/c = 6/a simplifies to 3a = 6c ⇒ a/c = 2, so the first and third statements are equivalent. The angle statement would be true only if ∠A = 80° (since ∠D corresponds to ∠A).
Reason: ABC ~ DEF means A↔D, B↔E, C↔F. So corresponding sides are AB↔DE, BC↔EF, AC↔DF. Thus BC corresponds to EF, not DE, so BC cannot be congruent to DE (unless the scale factor happened to be 1).
Also note 3/c = 6/a simplifies to 3a = 6c ⇒ a/c = 2, so the first and third statements are equivalent. The angle statement would be true only if ∠A = 80° (since ∠D corresponds to ∠A).
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