Question

prove: eg = ab + fg
statements reasons

1. ab ≅ bc 1. given
2. bc ≅ ef 2. given
3. ab ≅ ef 3. transitive prop.
4. ab = ef 4. def. of ≅ segs.
5. eg = ef + fg 5. seg. addition
6. eg = ab + fg 6. substitution

it is part of the given information.
it is part of the argument.
it is the conclusion.
it is an assumption.

Explanation:

Step1: Analyze the proof structure

We have a series of statements and reasons to prove $EG = AB+FG$.

Step2: Check the role of $AB = EF$

From the given statements, $AB = EF$ is derived from $AB\cong EF$ (by the definition of congruent segments). It is used later for substitution in the segment - addition statement $EG = EF + FG$ to get $EG=AB + FG$. This statement is part of the logical argument that leads to the conclusion.

Answer:

It is part of the argument.