Geometry Theorem Proof

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Prove that an interior angle bisector of any triangle divides the side of the triangle opposite the angle into segments proportional to the adjacent sides.

Statement Reason
1 Bisector of angle ABC intersects line AC at a point D between A and C. Betweenness axiom. (The angle bisector is between the ray BA and the ray BC.)
2 Angle ABD equals angle DBC. Definition of angle bisector.
3 There is a line L through A parallel to the line BD. Existence of parallel ...