Question

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1. b is the midpointac.

given

1. (overline{ab}congoverline{bc})

definition of midpoint
3.
definition of congruent segments

1. (ab + bc = ac)

segment addition postulate

1. (bc + bc = ac)

substitution property of equality

1. (2bc = ac)

addition property of equality
q.e.d.

1. the figure below shows segments (overline{ac}) and (overline{df}) such that b and e are points on the segments respectively and that (overline{ab}) is congruent to (overline{de}). determine the appropriate statement for the reason in step 4.

Explanation:

Step1: Recall congruent - segments property

If $\overline{AB}\cong\overline{DE}$, then $AB = DE$ by the definition of congruent segments.

Step2: Apply segment - addition postulate

For segment $\overline{AC}$, we have $AB + BC=AC$ and for segment $\overline{DF}$, we have $DE + EF = DF$. Since $AB = DE$, we can substitute in the equations. But the question asks for the statement for the reason "Segment Addition Postulate" which is related to the segments on the same line. For segment $\overline{AC}$, the statement is $AB + BC = AC$.

Answer:

$AB + BC = AC$