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The image shows a geometry problem involving the segment addition axiom. The given diagram shows a line segment with points \( A \), \( B \), and \( C \), where:

- \( AB = ? \) (unknown)
- \( BC = 10 \)
- \( AC = 12 \)

To find the length of segment \( AB \), we can use the **segment addition axiom**, which states:

\[
AB + BC = AC
\]

Substituting the known values:

\[
AB + 10 = 12
\]

Solving for \( AB \):

\[
AB = 12 - 10 = 2
\]

Thus, the length of segment \( AB \) is **2 units**.

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Would you like further explanation or details? Here are five related questions for further exploration:

1. What is the segment addition axiom in geometry?
2. How would the solution change if \( BC \) were longer than \( AC \)?
3. What happens if the total segment length \( AC \) is not greater than \( BC \)?
4. Can you apply the segment addition axiom in three-dimensional geometry?
5. How can you use the segment addition axiom to solve problems involving multiple points on a line?

**Tip**: Always double-check given values and their relationships when using geometric axioms to ensure accurate solutions.

Find the length of segment AB, given that BC = 10 and AC = 12, using the segment addition axiom.

Solve a geometry problem using the segment addition axiom where AB + BC = AC. Given BC = 10 and AC = 12, find the length of AB. This problem involves key geometric concepts like the segment addition axiom and basic algebraic steps. Suitable for students in Grades 6-8.

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