Question

hf = 8
gf = 28
find the value of x and gh.
segment addition postulate: gh + hf = gf
press the hotspot and type your answer. do not include symbols, just provide your numerical answer.
x =
gh =

Explanation:

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<reasoning>

Set up the segment addition equation

Using the Segment Addition Postulate:
\[GH + HF = GF\]
Substitute the given values:
\[2x + 8 = 28\]

Solve for x

Subtract 8 from both sides:
\[2x = 20\]
Divide by 2:
\[x = 10\]

Calculate the length of GH

Substitute \(x = 10\) into the expression for \(GH\):
\[GH = 2x = 2(10) = 20\]
</reasoning>

<answer>
Find the value of \(x\) and \(GH\).

Segment Addition Postulate: \(GH + HF = GF\)

\(x =\) <blank>10</blank>

\(GH =\) <blank>20</blank>
</answer>

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"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Geometry",
"Segment Addition Postulate"
]
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</post_analysis>

Answer:

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</pre_analysis>

<reasoning>

Set up the segment addition equation

Using the Segment Addition Postulate:
\[GH + HF = GF\]
Substitute the given values:
\[2x + 8 = 28\]

Solve for x

Subtract 8 from both sides:
\[2x = 20\]
Divide by 2:
\[x = 10\]

Calculate the length of GH

Substitute \(x = 10\) into the expression for \(GH\):
\[GH = 2x = 2(10) = 20\]
</reasoning>

<answer>
Find the value of \(x\) and \(GH\).

Segment Addition Postulate: \(GH + HF = GF\)

\(x =\) <blank>10</blank>

\(GH =\) <blank>20</blank>
</answer>

<post_analysis>
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"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Geometry",
"Segment Addition Postulate"
]
}
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