Question

$\overline{jk} \cong \overline{gm}$, $\angle fkg \cong \angle hji$, and $\angle fgk \cong \angle ihj$. complete the proof that $\overline{hi} \cong \overline{fg}$.

statement	reason
2. $\angle fkg \cong \angle hji$	given
3. $\angle fgk \cong \angle ihj$	given
4. $gk = jk + gj$	additive property of length
5. $hj = gh + gj$	additive property of length
6. $gk = gh + gj$
7. $hj = gk$	transitive property of equality
8. $\triangle fgk \cong \triangle ihj$	asa
9. $\overline{hi} \cong \overline{fg}$	cpctc

Explanation:

Step1: Substitute $\overline{JK} \cong \overline{GH}$

Since $\overline{JK} \cong \overline{GH}$, their lengths are equal: $JK = GH$. Substitute this into the equation from Step 4 ($GK = JK + GJ$).
<Expression>
$GK = GH + GJ$
</Expression>

Step2: Identify reason for Step 6

The substitution uses the given congruence of $\overline{JK}$ and $\overline{GH}$ to replace $JK$ with $GH$ in the length equation.
<Expression>
Reason: Substitution Property of Equality
</Expression>

Answer:

Substitution Property of Equality