Final answer:
The angles ∠ACB and ∠ADB are congruent because they are subtended by the same arc in a circle, with (AC) and (AD) being radii of the same circle.
Step-by-step explanation:
To determine why ∠ACB ≅ ∠ADB in the straightedge and compass construction of a regular hexagon, we must consider the underlying geometric principles. The key here is to recognize that both angles are subtended by the same arc in a circle, and that the sides of the angles are related by the radii of the same circle.
Option (a) and option (c) are essentially the same stating that (AC) and (AD) are radii of the same circle. This means that points A, C, and D all lie on the circumference of the same circle with the center at point A. Given this, ∠ACB and ∠ADB are both angles that subtend the same arc AB and thus, by the Inscribed Angle Theorem, they must be congruent.
Therefore, the correct response is that (AC) and (AD) are radii of the same circle, which tells us the angles are congruent. This is a fundamental concept in circle geometry which ensures that every regular hexagon constructed using a straightedge and compass will have its corners lying on the circumference, leading to congruent inscribed angles.