Question

1. segments $overline{de}$, $overline{fg}$ and $overline{hj}$ are shown in the accompanying figure. it is known that $overline{de}$ is congruent to $overline{fg}$ and $overline{fg}$ is congruent to $overline{hj}$. describe the statement in step 4 of the proof.

step\treason
$overline{ab}congoverline{de}$\tgiven

1. $ac = df$, $ab = de$\tdefinition of congruent segments
2. $ab + bc=ac$\tsegment addition postulate
3. ___\tsubstitution property of equality

q.e.d.

Explanation:

Step1: Recall given information

We know $AB\cong DE$ and $AC = DF$ and $AB + BC=AC$.

Step2: Apply substitution

Since $AB\cong DE$ and $AC = DF$ and $AB + BC=AC$, by substitution property of equality, we substitute $AB$ with $DE$ and $AC$ with $DF$. Just as $AB + BC=AC$, for the other - set of congruent segments, if we consider the segments related to $DE$ and $DF$, we have $DE + EF=DF$ (assuming the appropriate segment - addition relationship in the context of the figure, similar to $AB + BC=AC$).

Answer:

$DE + EF=DF$