The Angle Bisector Theorem, explaining how an internal angle bisector divides the opposite side in the ratio of the other two sides, with a proof and a sample problem.

Diagram illustrating the Angle Bisector Theorem, showing a triangle ABC with an angle bisector AD dividing side BC into segments BD and DC, and demonstrating the ratio AB/AC = BD/DC. The image includes a proof using parallel lines and similar triangles, and a worked example to find the length of BD given AB = 5, AC = 7, and BC = 6.