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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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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.