Answer
$G$
Work Step by Step
The corollary to the Side-Splitter Theorem states that if three parallel lines cut through two transversals, then the sections cut by the parallel lines will be proportional.
Let's check to see if the sides are proportional to one another.
We are given that $x = 3$.
$\frac{3}{12}$
Divide both the numerator and denominator by their greatest common factor, $3$:
$\frac{1}{4}$
Let's look at the segments cut by the other transversal:
$\frac{2}{8}$
Divide both the numerator and denominator by their greatest common factor, $2$:
$\frac{1}{4}$
The ratios of segments are equal to one another; therefore, the corollary to the Side-Splitter Theorem applies. The answer is option $G$.
