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In triangle ABC the point D lies on side AB and the point E lies on side AC. For which one of these sets of measurements is DE parallel to BC?

Competition practiceGeometry
  • AAD = 4, DB = 6, AE = 5, EC = 8
  • BAD = 3, DB = 5, AE = 6, EC = 10
  • CAD = 5, DB = 4, AE = 8, EC = 10
  • DAD = 2, DB = 7, AE = 7, EC = 2

Step-by-Step Solution

By the converse of the basic proportionality theorem, DE ∥ BC exactly when AD : DB = AE : EC. Test each set: 4/6 = 0.67 against 5/8 = 0.63, no; 3/5 = 0.6 against 6/10 = 0.6, yes; 5/4 = 1.25 against 8/10 = 0.8, no; 2/7 against 7/2, no. Only the second set works. The last set is the trap of matching AD with EC and DB with AE — the two numerators must both be the pieces next to A.
Answer: B) AD = 3, DB = 5, AE = 6, EC = 10

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