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Angle Bisector Theorem Calculator . Triangle vertices are usually named a, b, and c. It follows that the length of a and b can also be. Perpendicular Bisector Theorem GeoGebra from www.geogebra.org • simple math in any numeral system. As you can see in the picture below, the angle bisector theorem states that the angle bisector, like segment ad in the picture below, divides the sides of the a triangle proportionally. According to the angle bisector theorem: