Here are the steps to prove that triangles POT and QOR are congruent:
1) The circle has center O and radius 1, so OP = OQ = 1 (radius of the circle)
2) Angles POQ and ROQ are inscribed in the same arc PQ, so they are congruent (inscribed angle theorem)
3) Triangle POT is isosceles with OP = PT
4) Triangle QOR is isosceles with OQ = QR
5) By Side-Angle-Side postulate (SAS), triangles POT and QOR are congruent since:
a) OP = OQ (both radii are 1)
b)∠POQ ≅ ∠ROQ (inscribed angles are congruent)
c) PT = QR (corresponding sides of isosceles triangles)
In summary, triangles POT and QOR are congruent by the Side-Angle-Side congruence postulate since they have 2 matching sides (OP and OQ) and a matching acute angle (POQ and ROQ).