A rectangle has 2 pairs of parallel sides.

Any 2 sides of a rectangle are congruent.

Congruent parts of congruent figures are corresponding.

Corresponding parts of congruent figures are congruent.

Triangles ABC and DCB are congruent by the Angle-Angle Triangle Congruence Theorem.

Triangles ABC and BCD are congruent by the Angle-Side-Angle Triangle Congruence Theorem

Triangles ABC and BCD are congruent by the Side-Side-Side Triangle Congruence Theorem.

Triangles ABC and DCB are congruent by the Side-Angle-Side Triangle Congruence Theorem.

Triangles ABC and DCB are congruent by the Side-Side-Side Triangle Congruence Theorem.

Rotate GHJ using center G until GH is lined up with ST and then reflect over a line halfway between G'H'J' and STU.

Translate GHJ by the directed line segment GS. Rotate G'H'J' using S as the center by angle H'ST. Reflect G''H''J'' over ST.

Translate GHJ by the directed line segment GT. Rotate G'H'J' using T as the center by angle H'TS. Reflect G''H''J'' over ST.

Translate GHJ by the directed line segment GS.Translate G'H'J' by the directed line segment H'T. Translate G''H''J'' by the directed line segment J''T.

The image of U and J are on the same side of ST and make the same angle with it at T.

The image of U and J are the same distance along the same ray from T.

The image of U and J will not coincide after reflection over ST.

Line ST is the perpendicular bisector of the segment connecting U and J, because the perpendicular bisector is determined by 2 points that are both equidistant from the endpoints of a segment.