AB is congruent to ST by the transitive property of congruence, which states if one segment is congruent to a second segment, and the second segment is congruent to a third segment, then the first and third are congruent as well.
The question involves proving that segment AB is congruent to segment ST, given that AB is congruent to JK, and JK is congruent to ST. The transitive property of congruence is the most straightforward way to prove this statement.
The transitive property of congruence states that if two segments are both congruent to a third segment, then they are congruent to each other. Since AB is congruent to JK, and JK is congruent to ST, we can conclude by transitivity that AB is congruent to ST. This proof does not require the use of the law of cosines, the Pythagorean theorem, nor the law of sines because it depends solely on the intrinsic properties of congruence.
Thus, by the transitive property, AB is indeed congruent to ST without the need of any additional geometric theorems or laws. This form of proof is both efficient and sufficient for demonstrating congruence between segments.