Explanation
The Angle Bisector Theorem states:
The angle bisector of a triangle divides the opposite side into segments proportional to the other two sides.
If ∠A is bisected, and D is on BC:
AB / AC = BD / DC
Example: Triangle with AB = 6, AC = 8, BD = x, DC = 4 → 6/8 = x/4 → x = 3