Answer
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.
Work Step by Step
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