To prove something using segment addition, we typically use the Segment Addition Postulate. This postulate states that if a point \( B \) lies on a line segment \( AC \), then the sum of the lengths of segments \( AB \) and \( BC \) is equal to the length of \( AC \).

### Statement of Segment Addition Postulate:
\[ AB + BC = AC \]

### Example Proof Using Segment Addition:

**Problem:** Prove that if point \( B \) lies between points \( A \) and \( C \) on a straight line, then \( AB + BC = AC \).

**Given:**
- Points \( A \), \( B \), and \( C \) are collinear.
- \( B \) lies between \( A \) and \( C \).

**To Prove:**
\[ AB + BC = AC \]

**Proof:**
1. **Start by identifying the segments:**  
   We have a line segment \( AC \) with point \( B \) between \( A \) and \( C \). Therefore, segments \( AB \) and \( BC \) exist, and \( AC \) is the entire segment from \( A \) to \( C \).

2. **Apply the Segment Addition Postulate:**  
   According to the Segment Addition Postulate, if a point \( B \) lies on a line segment \( AC \), then:
   \[
   AB + BC = AC
   \]

3. **Conclude the proof:**  
   Since the conditions of the Segment Addition Postulate are satisfied (i.e., point \( B \) lies between points \( A \) and \( C \)), we have:
   \[
   AB + BC = AC
   \]

Therefore, the statement is proven.

Would you like any more details or have any questions?

Here are 5 related questions:
1. How does the Segment Addition Postulate help in solving geometric proofs?
2. Can you provide an example where the Segment Addition Postulate is used in a coordinate plane?
3. What happens if point \( B \) does not lie between \( A \) and \( C \)?
4. How does the Segment Addition Postulate relate to the concept of betweenness?
5. Can the Segment Addition Postulate be applied to non-collinear points?

**Tip:** When solving problems involving segments, always check if you can apply the Segment Addition Postulate. This can simplify many geometric proofs.

Learn how to prove geometric statements using the Segment Addition Postulate. This example explains the proof that if point B lies between points A and C on a straight line, then AB + BC = AC. Suitable for students in Grades 8-10.

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