Final Answer:
3. ∠bde ≅ ∠abc; corresponding angles postulate
Explanation:
In this scenario, the correct statement and reason that accurately complete the proof are “3. ∠bde ≅ ∠abc; corresponding angles postulate.” According to the corresponding angles postulate, when a transversal intersects two parallel lines, the pairs of corresponding angles are congruent. In this case, the angles ∠bde and ∠abc are corresponding angles as they are on the same side of the transversal and between the parallel lines. Therefore, by the corresponding angles postulate, we can conclude that ∠bde ≅ ∠abc.
This conclusion is supported by the fact that when a transversal intersects two parallel lines, such as in this scenario, the corresponding angles formed are congruent. The corresponding angles postulate is a fundamental concept in geometry and is used to establish the relationship between angles formed by a transversal and parallel lines. By applying this postulate to the given scenario, we can confidently assert that ∠bde ≅ ∠abc.
Therefore, based on the corresponding angles postulate, we can accurately complete the proof by stating that “3. ∠bde ≅ ∠abc; corresponding angles postulate.” This aligns with the principles of geometry and provides a valid reasoning for the equality of these angles within the given context.