Explanation:
What is not indicated is that triangle DEF has been / will be constructed onto angle ABC, thus creating three pairs of parallel lines.
However, to furnish a proper geometrical proof, we need also to prove that these lines are parallel. The given "proof" assumes that the lines are parallel.
In any case, the following is the best we can do, under the given conditions.
A. AB/DE = AC/DF = BC/EF (given)
B. DF // AC (construction of DEF onto ABC
C. Angle A congruent angle D, and angle C congruent to angle F
(Corresponding angles of parallel lines)
D. ABC ~ DEF (AA similarity Theorem)