Problem
2018 AMC 8 Problem 20
In \triangle ABC, a point E is on \overline{AB} with AE=1 and EB=2. Point D is on \overline{AC} so that \overline{DE} \parallel \overline{BC} and point F is on \overline{BC} so that \overline{EF} \parallel \overline{AC}. What is the ratio of the area of CDEF to the area of \triangle ABC?
![[asy] size(7cm); pair A,B,C,DD,EE,FF; A = (0,0); B = (3,0); C = (0.5,2.5); EE = (1,0); DD = intersectionpoint(A--C,EE--EE+(C-B)); FF = intersectionpoint(B--C,EE--EE+(C-A)); draw(A--B--C--A--DD--EE--FF,black+1bp); label("$A$",A,S); label("$B$",B,S); label("$C$",C,N); label("$D$",DD,W); label("$E$",EE,S); label("$F$",FF,NE); label("$1$",(A+EE)/2,S); label("$2$",(EE+B)/2,S); [/asy]](/static/aops/0571cfd5e8f21ce8031af38df8ba2295bdf2449a.png)
\textbf{(A) } \frac{4}{9} \qquad \textbf{(B) } \frac{1}{2} \qquad \textbf{(C) } \frac{5}{9} \qquad \textbf{(D) } \frac{3}{5} \qquad \textbf{(E) } \frac{2}{3}
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