Question

step statement reason
1
2
3
note: is a segment.

Explanation:

Step1: Analyze the given information

We know that \(AB\cong CD\) (given). Also, \(BC\) is a common segment.

Step2: Use the segment addition postulate

By the segment addition postulate, \(AC = AB + BC\) and \(BD=CD + BC\). Since \(AB\cong CD\) (i.e., \(AB = CD\)) and \(BC = BC\) (reflexive property), we can substitute \(AB\) with \(CD\) in the equation for \(AC\). So, \(AC=CD + BC\).

Answer:

Segment Addition Postulate.