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 and Position: Points \( C \), \( A \), \( B \) are collinear, and \( A \) is between \( C \) and \( B \).
2. Apply Segment Addition Postulate: The segment addition postulate states that if a point \( A \) lies on a line segment \( CB \), then \( CA + AB = CB \).
3. Formulate the Sum: Using this postulate, the sum of \( CA \) and \( AB \) (as lengths) equals the length of \( CB \).

Answer:

Since points \( C \), \( A \), and \( B \) are collinear (lying on a straight line) with \( A \) between \( C \) and \( B \), the sum of the lengths of segment \( CA \) and segment \( AB \) is equal to the length of segment \( CB \). In other words, \( CA + AB = CB \).