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By the Basic Proportionality Theorem, AB/BF=AD/DC.

We have guessed that when an angle of a triangle is bisected, the opposite side is divided into segments that are proportional to the other sides.

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By the Basic Proportionality Theorem, AB/BF=AD/DC.

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  1. We have guessed that when an angle of a triangle is bisected, the opposite side is divided into segments that are proportional to the other sides. This statement is merely a conjecture, arrived at inductively. We need to reason deductively in order to be assured that this will always be the case, for all triangles.

  2. By the Basic Proportionality Theorem, AB/BF=AD/DC.

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