## Geometry: Common Core (15th Edition)

According to the side-splitter theorem, if a line is parallel to a side of a triangle and intersects the other two sides, then those two sides are divided proportionately. Let's set up a proportion for the sides whose values are given in the figure. If the ratios are equal to one another, then we can conclude that the red segments are parallel: $\frac{6}{10} = \frac{9}{15}$ Simplify each ratio by dividing the numerator and denominator by their greatest common factor: $\frac{3}{5} = \frac{3}{5}$ The ratios are equal to one another; therefore, the red segments are parallel to one another.