CPhill

I think it's asking you if the vector is correct proof, or not. 

Hint: it is. 

Sorry, guest.....I couldn't see 20 clearly [or I mis-read it].....but.....if it says that   AD = DB and AE = EC.....then the sides are cut propotionally by DE. That is, each side is bisected by DE. So, triangle ABC ~  triangle ADE.

By Euclid.....if the sides of a triangle are cut proportionally, the line joining the points of intersection is parallel to the remaining side......thus DE is parallel to DC....and we proved in (18) that, if this was so, the triangles were similar

If you are  interested, here's Euclid's proof :

http://aleph0.clarku.edu/~djoyce/java/elements/bookVI/propVI2.html