Question

in the following diagram, points c, a, and b are collinear. use complete sentences to describe the sum of ca and ab.

Explanation:

1. Identify collinearity: Points \( C \), \( A \), \( B \) are on a straight line, so the segment addition postulate applies.
2. Apply the postulate: For collinear points with \( A \) between \( C \) and \( B \), \( CA + AB = CB \).
3. Describe the sum: The sum of \( CA \) (distance from \( C \) to \( A \)) and \( AB \) (distance from \( A \) to \( B \)) is the distance from \( C \) to \( B \) (i.e., \( CB \)).

Answer:

The sum of the lengths of segment \( CA \) and segment \( AB \) is equal to the length of segment \( CB \). Since points \( C \), \( A \), and \( B \) are collinear (they lie on the same straight line) with \( A \) between \( C \) and \( B \), by the segment addition postulate, we have \( CA + AB = CB \). In words, if we start at point \( C \), move along the line to point \( A \) (a distance of \( CA \)), and then continue from point \( A \) to point \( B \) (a distance of \( AB \)), the total distance we have traveled from \( C \) to \( B \) is the sum of \( CA \) and \( AB \).