Question

statements
1 ( a b cong c d ; e d cong e b )
2 ( a b=c d ; e d=e b )
3 ( a e+e b=a b ; c e+e d=g d )
4 ( c e+e b=c d )
5 ( c e+e b=a e+e b )
6 ( c e=a e )
7 ( c e cong a e )
definition of midpoint
segment addition postulate
angie addition postulate
definition of congruent segments
3
4 substitution

1. transitive property
2. substitution

7 definition of congruent segments

Explanation:

Step1: Analyze the given statements

We have \(AB\cong CD\) and \(ED\cong EB\). By the definition of congruent segments, if two segments are congruent, then their lengths are equal. So, \(AB = CD\) and \(ED=EB\).

Step2: Consider the segment - addition postulate

The segment - addition postulate states that if we have a line segment \(AC\) with a point \(B\) between \(A\) and \(C\), then \(AB + BC=AC\). In our case, for segment \(AB\), if we consider a point \(E\) (assuming the relevant line - segment structure), \(AE + EB=AB\) and for segment \(CD\), \(CE + ED = CD\) (by the segment - addition postulate).

Answer:

Segment Addition Postulate