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Point [tex]$C$[/tex] is between points [tex]$A$[/tex] and [tex]$B$[/tex]. Then [tex]$AC + \ldots = AB$[/tex].

A. [tex]$CA$[/tex]
B. [tex]$AB$[/tex]
C. [tex]$CB$[/tex]
D. [tex]$ABC$[/tex]

Sagot :

GinnyAnsweridn
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]
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