1. **Problem Statement:** Given triangle RQT, S is the midpoint of segment RT, and U is the midpoint of segment QT. If the length of QR is 92, find the length of segment SU. 2. **Key Concept:** The segment connecting the midpoints of two sides of a triangle is parallel to the third side and its length is half the length of that third side. This is known as the Midsegment Theorem. 3. **Apply the Midsegment Theorem:** Since S and U are midpoints of RT and QT respectively, segment SU is parallel to side RQ and: $$ SU = \frac{1}{2} \times QR $$ 4. **Calculate SU:** Given $QR = 92$, substitute into the formula: $$ SU = \frac{1}{2} \times 92 = 46 $$ 5. **Answer:** The length of segment SU is 46.