## Geometry: Common Core (15th Edition)

According to the triangle-angle-bisector theorem, when a ray bisects the angle of a triangle, the opposite side is divided into two segments that are proportional to the remaining two sides of the triangle. Let's set up a proportion that compares the segments of the intersected side to the other two sides: $\frac{KL}{KM} = \frac{LW}{MW}$ According to a property of proportions, we can switch the means: $\frac{KL}{LW} = \frac{KM}{MW}$