1. **Problem statement:** In parallelogram PQRS, given that diagonal SQ = 26, find the length of segment ST, where T is the intersection of diagonals PR and SQ. 2. **Key property:** In any parallelogram, the diagonals bisect each other. This means that the point of intersection T divides each diagonal into two equal parts. 3. Since T is the midpoint of diagonal SQ, the lengths ST and TQ are equal. 4. Given that the entire diagonal SQ = 26, we can write: $$SQ = ST + TQ = 2 \times ST$$ 5. Solving for ST: $$ST = \frac{SQ}{2} = \frac{26}{2} = 13$$ 6. **Answer:** The length of segment ST is 13 units.