Question

ge abc shown, \\(\overline{de} \parallel \overline{bc}\\).
move options to the proof to show that \\(\overline{de}\\) divides \\(\overline{ab}\\) and \\(\overline{ac}\\) proportionally.

statement	reason
\\(\angle a \cong \angle a\\)	reflexive property
\\(\angle abc \cong \angle ade\\)	corresponding angles of \\(\underline{\quad}\\) are congruent.
\\(\triangle abc \sim \triangle ade\\)	angle - angle similarity
\\(\underline{\quad}\\)	corresponding sides of similar triangles are \\(\underline{\quad}\\).

options: parallel lines, congruent triangles, \\(\frac{ab}{ad} = \frac{ac}{ae}\\), \\(\overline{ab} \cong \overline{ac}; \overline{ad} \cong \overline{ae}\\), congruent, proportional

Explanation:

Step1: Fill first blank (parallel lines)

Corresponding angles of parallel lines are congruent.

Step2: Fill second blank (proportional)

Corresponding sides of similar triangles are proportional, leading to $\frac{AB}{AD} = \frac{AC}{AE}$.

Answer:

1. For the first blank: parallel lines
2. For the second blank: proportional
3. Final completed proportion: $\frac{AB}{AD} = \frac{AC}{AE}$