SAT Question 858809e7: Lines, Angles, and Triangles answer and explanation with Desmos solution

Choice B is correct. In the figure, $\overline{AE}$ intersects line $l$ and $\overline{EG}$, and alternate interior angles are both marked $x^{\circ }$. It follows that $\overline{EG}$ is parallel to line $l$. It’s given that line $l$ is parallel to line $j$, so $\overline{EG}$ is also parallel to line $j$. Thus, the following angles also have measure $x^{\circ }$: $\angle EFA$, $\angle ACD$, $\angle BAD$, and $\angle GFD$. Triangles $AEF$ and $ACD$ each have two angles with measure $x^{\circ }$, so triangles $AEF$ and $ACD$ are similar. It’s also given that $EF=0.5CD$, so $AF=0.5AD$. It follows that $AF=FD$. Triangles $DFG$ and $DAB$ each have one angle with measure $x^{\circ }$ and share $\angle FDG$, so triangles $DFG$ and $DAB$ are similar. Since $AF=FD$, it follows that $AD=2FD$, so $AB=2FG$. Substituting $2FG$ for $AB$ in statement I yields $2FG=2.25EF$. It's given that $FG=2.25CD$. Substituting $2.25CD$ for $FG$ and $0.5CD$ for $EF$ in the equation $2FG=2.25EF$ yields $2(2.25CD)=2.25(0.5CD)$, or $4.5CD=1.125CD$. Thus, statement I is not true. Since $AB=2FG$, it follows that $0.5AB=FG$, or $FG=0.5AB$. Therefore, statement II must be true. Substituting $0.5CD$ for $EF$, $2.25CD$ for $FG$, and $FD$ for $AF$ in statement III yields $\frac{0.5CD}{2.25CD}=\frac{FD}{FD}$, or $\frac{2}{9}=1$. Thus, statement III is not true. Therefore, statement II only must be true.