We know that ∠ SRT ≅ ∠ URT. What we have to show is that the sides that forms these angles in △ STR and △ UTR are congruent as well.
Let's start with the relatively easy one, TR. This side is shared by △ SRT and △ URT. Therefore, by the Reflexive Property of Congruence, we know this side is congruent in the triangles.
Finally, we have to show that SR ≅ UR. If we examine these sides, we notice that they actually make out the circle's radius. This means they are of the same length and therefore congruent.
Since we now know that two sides and the included angle of △ SRT are congruent to two sides and the included angle of △ URT, we can use the SAS Congruence Theorem to claim that these triangles are congruent.
