Question

1. in the figure below, what value of \\(x\\) will satisfy the midsegment theorem? (lesson 8.4) (1 point)

\\(g\\) is on \\(sr\\), \\(h\\) is on \\(rq\\).
\\(gh = 4x - 65\\)
\\(sq = 2x - 4\\)

Explanation:

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<reasoning>

Set up the midsegment equation

\[
2(4x - 65) = 2x - 4
\]

Solve for x

\[

$$\begin{aligned} 8x - 130 &= 2x - 4 \\ 6x &= 126 \\ x &= 21 \end{aligned}$$

\]
</reasoning>

<answer>
In the figure below, what value of x will satisfy the midsegment theorem? <blank>21</blank>
</answer>

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Answer:

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<reasoning>

Set up the midsegment equation

\[
2(4x - 65) = 2x - 4
\]

Solve for x

\[

$$\begin{aligned} 8x - 130 &= 2x - 4 \\ 6x &= 126 \\ x &= 21 \end{aligned}$$

\]
</reasoning>

<answer>
In the figure below, what value of x will satisfy the midsegment theorem? <blank>21</blank>
</answer>

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