To solve this problem, we need to apply the segment addition postulate, which states:
If point [tex]\( C \)[/tex] is between points [tex]\( A \)[/tex] and [tex]\( B \)[/tex], then the sum of segments [tex]\( AC \)[/tex] and [tex]\( CB \)[/tex] is equal to the segment [tex]\( AB \)[/tex].
Let's analyze the given options:
1. Option A: [tex]\( C A \)[/tex]
This option would imply that [tex]\( AC + CA = AB \)[/tex]. However, [tex]\( C A \)[/tex] and [tex]\( A C \)[/tex] represent the same segment, and we need to add segments to other adjoining segments, not the same one again.
2. Option B: [tex]\( A B \)[/tex]
This option would imply that [tex]\( AC + AB = AB \)[/tex]. This is incorrect, because [tex]\( C \)[/tex] is still between [tex]\( A \)[/tex] and [tex]\( B \)[/tex], and adding the whole segment [tex]\( AB \)[/tex] to part of it makes no sense.
3. Option C: [tex]\( C B \)[/tex]
This option implies that [tex]\( AC + CB = AB \)[/tex]. This is precisely correct as per the segment addition postulate: the sum of the parts [tex]\( AC \)[/tex] and [tex]\( CB \)[/tex] equals the whole segment [tex]\( AB \)[/tex].
4. Option D: [tex]\( A B C \)[/tex]
This is not a valid segment relation and does not align with the segment addition postulate.
Therefore, the correct choice is:
Option C: [tex]\( C B \)[/tex]
So, the complete correct statement is:
[tex]\( AC + CB = AB \)[/tex]
