We can conclude that △COS is isosceles and ∠CAT ≅ ∠CTA based on the given information. We cannot determine the congruence of △OAC and △STC or the isosceles property of △CAS. Options A and D is the right choice.
Based on the given information and the diagram, we can conclude the following:
A. △COS is isosceles.
This is true because ∠O ≅ ∠S, which are base angles of △COS. Therefore, the sides OC and OS must be congruent by the Angle-Angle (AA) Congruence Criterion.
B. △OAC ≅ △STC
This is not necessarily true. We are only given that two pairs of corresponding angles are congruent, but not that any sides are congruent. Therefore, we cannot conclude that the triangles are congruent by the AA Similarity Criterion.
C. △CAS is isosceles.
This is not necessarily true. We cannot determine the congruence of any of the sides or angles in △CAS based on the given information.
D. ∠CAT ≅ ∠CTA
This is true because they are vertical angles. Vertical angles are always congruent by definition.
Therefore, the only correct options are A and D.