Final answer:
The proof utilizes the SAS Postulate to establish congruence between △ASHD and △ASTD, with the shared side SD, the congruent sides SH and ST, and the right angles at D.
Step-by-step explanation:
The student's question appears to relate to geometric proofs, specifically proving the congruency of two triangles - ASDH and ASTD. The given conditions are that segment SD is perpendicular to HT and segments SH and ST are congruent.
To prove triangle congruence, we must show that they have three corresponding congruent parts, which may belong to the categories of sides or angles. As the given information specifies that SD is perpendicular to HT, we know that angles SDH and SDT are right angles (Definition of right angle). Since the problem states that SH is congruent to ST, and we have SD being shared by both triangles, we now have two sides and the included angle that are congruent, which aligns with the criteria for the SAS Postulate (Side-Angle-Side).
By applying the Reflexive Property of congruence to side SD (which is shared by both triangles), and considering that both triangles have right angles by definition, along with SH ≡ ST, we can conclude that △ASHD ≡ △ASTD through the SAS Postulate.