Question

write the segment addition postulate. name the segments from left to right using capital letters with no spaces between them.

\\(ac + cb = ab\\)

determine the segment lengths.

\\(ac = 8\\)
\\(cb = 3\\)

substitute in the segment lengths to find ab.

\\(8 + 3 = ab\\)
\\(11 = ab\\)

Explanation:

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],
"new_concepts": [
"Segment Addition Postulate"
],
"current_concepts": [
"Rays and Segments",
"Segment Addition Postulate"
]
}
</pre_analysis>

<reasoning>

Identify the points on the coordinate plane

We find the coordinates of points \(A\), \(C\), and \(B\) on the horizontal line \(y = -4\):

• Point \(A\) is at \((-2, -4)\).
• Point \(C\) is at \((6, -4)\).
• Point \(B\) is at \((9, -4)\).

Apply the Segment Addition Postulate

Using Rays and Segments, since point \(C\) lies between points \(A\) and \(B\) on the line segment \(AB\), the Segment Addition Postulate states:
\[
AC + CB = AB
\]

Calculate the individual segment lengths

Find the horizontal distance between the points:

• Length of \(AC\):

\[
AC = 6 - (-2) = 8
\]

• Length of \(CB\):

\[
CB = 9 - 6 = 3
\]

Substitute the lengths to find the total length

Substitute the calculated lengths into the postulate equation:
\[
8 + 3 = AB
\]
\[
11 = AB
\]
</reasoning>

<answer>
Write the Segment Addition Postulate. Name the segments from left to right using capital letters with no spaces between them.
<blank>AC</blank> + <blank>CB</blank> = AB

Determine the segment lengths.
AC = <blank>8</blank>
CB = <blank>3</blank>

Substitute in the segment lengths to find AB.
<blank>8</blank> + <blank>3</blank> = AB
<blank>11</blank> = AB
</answer>

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

Answer:

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"concepts_used": [
"Rays and Segments"
],
"new_concepts": [
"Segment Addition Postulate"
],
"current_concepts": [
"Rays and Segments",
"Segment Addition Postulate"
]
}
</pre_analysis>

<reasoning>

Identify the points on the coordinate plane

We find the coordinates of points \(A\), \(C\), and \(B\) on the horizontal line \(y = -4\):

• Point \(A\) is at \((-2, -4)\).
• Point \(C\) is at \((6, -4)\).
• Point \(B\) is at \((9, -4)\).

Apply the Segment Addition Postulate

Using Rays and Segments, since point \(C\) lies between points \(A\) and \(B\) on the line segment \(AB\), the Segment Addition Postulate states:
\[
AC + CB = AB
\]

Calculate the individual segment lengths

Find the horizontal distance between the points:

• Length of \(AC\):

\[
AC = 6 - (-2) = 8
\]

• Length of \(CB\):

\[
CB = 9 - 6 = 3
\]

Substitute the lengths to find the total length

Substitute the calculated lengths into the postulate equation:
\[
8 + 3 = AB
\]
\[
11 = AB
\]
</reasoning>

<answer>
Write the Segment Addition Postulate. Name the segments from left to right using capital letters with no spaces between them.
<blank>AC</blank> + <blank>CB</blank> = AB

Determine the segment lengths.
AC = <blank>8</blank>
CB = <blank>3</blank>

Substitute in the segment lengths to find AB.
<blank>8</blank> + <blank>3</blank> = AB
<blank>11</blank> = AB
</answer>

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