Question

r is the midpoint of \\(\overline{qs}\\) and t is the midpoint of \\(\overline{su}\\). if \\(rt = 9\\), what is \\(qu\\)? \\(qu = \square\\)

Explanation:

Step1: Identify the Midline Theorem

In a triangle, the segment connecting the midpoints of two sides is parallel to the third side and half as long. Here, \( R \) is the midpoint of \( \overline{QS} \) and \( T \) is the midpoint of \( \overline{SU} \), so \( RT \) is the midline of \( \triangle QSU \).

Step2: Apply the Midline Theorem

By the midline theorem, \( RT=\frac{1}{2}QU \). We know \( RT = 9 \), so we can solve for \( QU \) by multiplying both sides of the equation by 2.
\[ QU = 2\times RT \]
\[ QU = 2\times9 \]
\[ QU = 18 \]

Answer:

\( 18 \)