Question

$\overline{ts}$ is the midsegment of trapezoid $hjkl$. if $kl = 17$ and $jh = 9$, find $st$. round your answer to nearest tenth, if necessary.

Explanation:

Step1: Recall the midsegment theorem for trapezoids.

The midsegment (or median) of a trapezoid is the segment that connects the midpoints of the non - parallel sides. The length of the midsegment \( TS \) of a trapezoid is equal to the average of the lengths of the two bases. The formula for the length of the midsegment \( m \) of a trapezoid with bases of lengths \( b_1 \) and \( b_2 \) is \( m=\frac{b_1 + b_2}{2} \).

In trapezoid \( HJKL \), the two bases are \( JH \) and \( KL \) with lengths \( JH = 9 \) and \( KL=17 \), and \( TS \) is the midsegment.

Step2: Substitute the values of the bases into the formula.

Substitute \( b_1 = 9 \) and \( b_2=17 \) into the formula \( m=\frac{b_1 + b_2}{2} \).
\[
TS=\frac{9 + 17}{2}=\frac{26}{2}=13
\]

Answer:

\( 13 \)