attitude.freak4u wrote:A triangle has three corners A,B and C. A line parallel to BC connects the sides AB and AC. What is the ratio of DE:BC?
1) AD=DB
2) Height of ADE = Height of ABC
This question has just one thing missing and that is the line parallel to BC connects the sides AB and AC in D and E respectively.
This uses the BPT (Basic Proportionality Theorem) in triangles. must revise we all
(1) When AD = DB, the problem reduces from the BPT (Basic Proportionality Theorem) to MPT (Mid Point Theorem) in triangles, and in that case a side of the bigger of the two similar triangles so obtained is twice of the corresponding side of the smaller of the two similar triangles so obtained, and hence, DE:BC = 1:2. Sufficient
(2) Ambiguity starts from here, this is possible only when the bases DE and BC are coinciding, DE:BC = 1:1. Seems sufficient, but it contradicts with (1)
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D, if contradiction within the statements could be overlooked by a mass[/spoiler]