Final Answer:
The correct proof to show that GH is perpendicular to DE is by the Corresponding Angles Postulate. Hence, the correct option is b).
Step-by-step explanation:
The Corresponding Angles Postulate states that when a transversal intersects two parallel lines, the corresponding angles are congruent. In this scenario, BC is parallel to DE, and angle GAC is approximately equal to angle AFD. According to the Corresponding Angles Postulate, this implies that the angles GH and DEC are corresponding angles, and they are congruent. Since GH and DEC are corresponding and congruent, and DE is parallel to BC, GH must be perpendicular to DE. This proof establishes the perpendicular relationship between GH and DE based on the congruence of corresponding angles.
While other options such as the Alternate Interior Angles Theorem and the Angle Bisector Theorem are valid theorems, they are not directly applicable to the given scenario. The Alternate Interior Angles Theorem is used when a transversal intersects two parallel lines, and the Angle Bisector Theorem involves the division of an angle into two congruent angles.
In this case, the Corresponding Angles Postulate is more fitting as it specifically addresses the relationship between corresponding angles in parallel lines. The Converse of the Corresponding Angles Postulate is not necessary here, as the original postulate itself is sufficient to establish the perpendicular relationship between GH and DE.