Final answer:
Without the full context of the geometric proof problem, such as a diagram or additional given information, it is not possible to provide the missing statement and reasons with certainty. Typical proof steps involve applying congruence theorems or angle properties, but these cannot be verified for this specific question. a) Angle-side-angle (ASA) is correct answer.
Step-by-step explanation:
The student is asked to complete a geometric proof to show that ∠SHD = ∠STD, given that ∠AHD = ∠ATD. However, without the specific details of the initial question, such as a figure or additional given information, it is not possible to provide the missing statement and reasons with certainty.
In a typical geometric proof, the steps would include identifying relevant theorems and postulates, such as the angle-side-angle (ASA) criterion for triangle congruence, the corresponding angles postulate, the alternate interior angles theorem, or the angle addition postulate.
But without the context of a diagram or additional givens, no definitive answer can be provided.
For example, if ∠AHD and ∠ATD are given as equal and we know that segment HD is congruent to segment TD, and segment AD is common to both triangles, then triangle AHD could be congruent to triangle ATD based on the ASA congruence theorem, which might then imply ∠SHD is congruent to ∠STD. However, this is speculative without the full context of the problem.