Question

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s is the midpoint of \\(\overline{rt}\\) and q is the midpoint of \\(\overline{ru}\\). if \\(tu = 42\\), what is \\(qs\\)? \\(qs = \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, \( S \) is the midpoint of \( \overline{RT} \) and \( Q \) is the midpoint of \( \overline{RU} \), so \( \overline{QS} \) is the midline of \( \triangle RTU \).

Step2: Apply the Midline Theorem

The midline \( QS \) should be half the length of the third side \( TU \). Given \( TU = 42 \), we calculate \( QS=\frac{1}{2}\times TU \).

Step3: Calculate \( QS \)

Substitute \( TU = 42 \) into the formula: \( QS=\frac{1}{2}\times42 = 21 \).

Answer:

\( 21 \)