Subjects geometry

Midsegment Length Ef282F

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1. **State the problem:** We are given triangle $\triangle QST$ with $RU$ as a midsegment. We know the length of side $ST = 8$, and we need to find the length of the midsegment $RU$. 2. **Recall the midsegment theorem:** In a triangle, a midsegment connecting the midpoints of two sides is parallel to the third side and its length is half the length of that third side. 3. **Apply the theorem:** Since $RU$ is a midsegment parallel to $ST$, its length is half of $ST$. 4. **Calculate:** $$RU = \frac{1}{2} \times ST = \frac{1}{2} \times 8 = 4$$ 5. **Conclusion:** The length of the midsegment $RU$ is $4$.