Question

1206310_geometry_h_cfa_chapter 2_2025 - 2026
two students are discussing the relationship between points and segments on a number line.
student a: \if point c lies on $overline{ab}$, then $overline{ac}+overline{cb}=overline{ab}$ based on the segment addition postulate.\
student b: \if $overline{ac}+overline{cb}=overline{ab}$, then c is the midpoint of $overline{ab}$.\
which two of the following statements are true?
□ student as statement is valid.
□ student as statement is invalid when c is not the midpoint of $overline{ab}$.
□ student as statement is invalid.
□ student bs statement is valid.
□ student bs statement is invalid because when point c is not the midpoint, the segment addition postulate still holds true.

Explanation:

Step1: Recall segment - addition postulate

The segment - addition postulate states that if a point $C$ lies on a line segment $\overline{AB}$, then $\overline{AC}+\overline{CB}=\overline{AB}$, regardless of whether $C$ is the mid - point of $\overline{AB}$ or not. So Student A's statement is valid.

Step2: Analyze Student B's statement

The equation $\overline{AC}+\overline{CB}=\overline{AB}$ is true for any point $C$ on $\overline{AB}$, not just when $C$ is the mid - point. The mid - point of $\overline{AB}$ is a special case where $\overline{AC}=\overline{CB}$. So Student B's statement is invalid.

Answer:

Student A's statement is valid.
Student B's statement is invalid because when point $C$ is not the midpoint, the segment addition postulate still holds true.