Question

The sum of the lengths of line segments AB and BC is the length of line segment AC.

Short answer

By applying the Segment Addition Postulate, we have proven that the sum of the lengths of line segments AB and BC is equal to the length of line segment AC: \(|AB| + |BC| = |AC|\).

Step-by-step solution

Understand the Problem

As mentioned in the analysis, we need to show that the sum of the lengths of line segments AB and BC is equal to the length of line segment AC. In other words, we need to prove that AB + BC = AC.

Express the Given Information Algebraically

Let's use variables to represent the lengths of the line segments. We can let: \(x = |AB|\), \(y = |BC|\), and \(z = |AC|\). Our goal is to prove that x + y = z.

Use the Segment Addition Postulate

According to the Segment Addition Postulate, if three points A, B, and C are collinear and B is between A and C, then |AB| + |BC| = |AC|. In our case, we can express this as: x + y = z

State the Conclusion

By applying the Segment Addition Postulate, we have proven that the sum of the lengths of line segments AB and BC is equal to the length of line segment AC: x + y = z or |AB| + |BC| = |AC|.