Question

find the segment lengths.

fg =
hi =
gi =

Explanation:

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"concepts_used": [
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<reasoning>

Identify the given segment lengths

Using the Segment Addition Postulate knowledge point
\[

$$\begin{aligned} &GH = 8\\ &FH = 20\\ &FI = 31 \end{aligned}$$

\]

Calculate the length of FG

Using the Segment Addition Postulate knowledge point
\[

$$\begin{aligned} &FG + GH = FH\\ &FG + 8 = 20\\ &FG = 12 \end{aligned}$$

\]

Calculate the length of HI

Using the Segment Addition Postulate knowledge point
\[

$$\begin{aligned} &FH + HI = FI\\ &20 + HI = 31\\ &HI = 11 \end{aligned}$$

\]

Calculate the length of GI

Using the Segment Addition Postulate knowledge point
\[

$$\begin{aligned} &GI = GH + HI\\ &GI = 8 + 11\\ &GI = 19 \end{aligned}$$

\]
</reasoning>

<answer>
Find the segment lengths.

FG = <blank>12</blank>

HI = <blank>11</blank>

GI = <blank>19</blank>
</answer>

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"question_type": "Fill-in-the-blank",
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Answer:

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<reasoning>

Identify the given segment lengths

Using the Segment Addition Postulate knowledge point
\[

$$\begin{aligned} &GH = 8\\ &FH = 20\\ &FI = 31 \end{aligned}$$

\]

Calculate the length of FG

Using the Segment Addition Postulate knowledge point
\[

$$\begin{aligned} &FG + GH = FH\\ &FG + 8 = 20\\ &FG = 12 \end{aligned}$$

\]

Calculate the length of HI

Using the Segment Addition Postulate knowledge point
\[

$$\begin{aligned} &FH + HI = FI\\ &20 + HI = 31\\ &HI = 11 \end{aligned}$$

\]

Calculate the length of GI

Using the Segment Addition Postulate knowledge point
\[

$$\begin{aligned} &GI = GH + HI\\ &GI = 8 + 11\\ &GI = 19 \end{aligned}$$

\]
</reasoning>

<answer>
Find the segment lengths.

FG = <blank>12</blank>

HI = <blank>11</blank>

GI = <blank>19</blank>
</answer>

<post_analysis>
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"knowledge_point": [
"Mathematics",
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"Segment Addition Postulate"
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