Final answer:
Option 4, stating that ∠DCE ≅ ∠DAB by construction, implies that AB and CD are parallel by using properties of alternate interior angles or corresponding angles, which are congruent when lines are parallel.
Step-by-step explanation:
In the context of straightedge and compass constructions, we utilize properties of geometry to establish relationships between angles and lines. When constructing a parallel line to AB such that CD is parallel to it, we do this through a series of geometric steps that guarantee the parallelism. To prove that lines AB and CD are parallel, we must rely on the properties of alternate interior angles or corresponding angles being congruent, which stems from Euclid's parallel postulate.
Of the options provided, saying "∠DCE ≅ ∠DAB by construction" (option 4) is relevant because if angle DCE is congruent to angle DAB, and they are situated such that one is an alternate interior angle or corresponding angle to the other (with line EC and AD being transversals), this would imply that AB and CD are parallel according to the Alternate Interior Angles Theorem or the Corresponding Angles Postulate. The options you provided do not directly connect the congruency of angles to the parallelism of lines without knowing their position in the configuration, but option 4 suggests that a key angle relationship was established by construction, which is often a step in demonstrating parallelism.