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To solve question 10, we are tasked with using the **Segment Addition Postulate** to show that:

\[
AE = AB + BC + CD + DE
\]

Let's break this down using the Segment Addition Postulate, which states that if point \( B \) lies between points \( A \) and \( C \) on a line, then the sum of segments \( AB \) and \( BC \) is equal to the entire segment \( AC \). We apply this idea to the points \( A \), \( B \), \( C \), \( D \), and \( E \).

### Step-by-Step Breakdown:

- According to the Segment Addition Postulate, for the points given, we can add the lengths of each consecutive segment to get the total length \( AE \).
- The points on the number line are \( A \), \( B \), \( C \), \( D \), and \( E \), and their respective segments are labeled as \( AB \), \( BC \), \( CD \), and \( DE \).
  
We can add the lengths of each segment:

\[
AE = AB + BC + CD + DE
\]

This is exactly what the Segment Addition Postulate tells us. Thus, by adding all the individual segments, we get the total length of segment \( AE \), proving the equation.

Would you like further details or have any other questions about this?

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Here are 5 related questions:
1. How does the Segment Addition Postulate apply to more than two segments?
2. If segment \( AB = 5 \), \( BC = 7 \), \( CD = 10 \), and \( DE = 12 \), what is the length of \( AE \)?
3. What would happen if one of the points, say \( C \), was not between the others?
4. How can you apply the Segment Addition Postulate in geometry proofs?
5. How is the Segment Addition Postulate different from the idea of distance in coordinate geometry?

**Tip**: The Segment Addition Postulate is essential for understanding how we measure distances in both geometry and number lines. Make sure to understand how it works with more complex diagrams as well!

How can you use the Segment Addition Postulate to show that AE = AB + BC + CD + DE?

Learn how to apply the Segment Addition Postulate to prove that AE = AB + BC + CD + DE. This problem focuses on understanding how the sum of smaller consecutive segments equals the length of the entire segment, suitable for students in Grades 6-8.

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