Question

prove: ( eg = ab + fg )

1. ( overline{ab} cong overline{bc} )
2. ( overline{bc} cong overline{ef} )
3. ( overline{ab} cong overline{ef} )
4. ( ab = ef )
5. ( eg = ef + fg )
6. ( eg = ab + fg )

• 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

The proof starts with given statements (\(\overline{AB}\cong\overline{BC}\), \(\overline{BC}\cong\overline{EF}\)), then uses properties (transitive property, definition of congruent segments, segment addition postulate) to reach the final statement \(EG = AB+FG\).

Step2: Classify each part

• The given information (\(\overline{AB}\cong\overline{BC}\), \(\overline{BC}\cong\overline{EF}\)) are the starting points.
• The intermediate steps (using transitive property, definition of congruent segments, segment addition postulate) are part of the argument.
• The statement \(EG = AB + FG\) is what is being proven, which is the conclusion.
• There are no assumptions made (all steps are based on given or properties).

Answer:

It is the conclusion.