Two proofs by symmetry of Thales's theorem

Proof 1: Since all segments of the parallelogram have are chords of a circle, they must share at least one line of symmetry with the circle, each highlighted with dotted green lines. These lines of symmetry are also shared by the parallelogram, meaning said parallelogram is a rectangle, proving Thales's theorem.

Proof 2: A̅C̅ and B̅B̅' are both a diameter of the same circle, as well as diagonals of the same parallelogram. A parallelogram with congruent diagonals must be a rectangle, also proving Thales's theorem.