Question

j is the midpoint of \\(\overline{fh}\\) and \\(\overline{gi}\\). complete the proof that \\(\triangle ghj \cong \triangle ifj\\).\
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	statement	reason	\
1	j is the midpoint of \\(\overline{fh}\\)	given	\
2	j is the midpoint of \\(\overline{gi}\\)	given	\
3	\\(\overline{fi} \cong \overline{gh}\\)	given	\
4	\\(\overline{fj} \cong \overline{hj}\\)	definition of midpoint	\
5	\\(\overline{gj} \cong \overline{ij}\\)	definition of midpoint	\
6	\\(\triangle ghj \cong \triangle ifj\\)	dropdown with options: aas, asa, cpctc, definition of congruence, sas, sss

Explanation:

Step1: Identify congruent sides

We have:

1. $\overline{GH} \cong \overline{FI}$ (Given)
2. $\overline{FJ} \cong \overline{HJ}$ (Midpoint definition)
3. $\overline{GJ} \cong \overline{IJ}$ (Midpoint definition)

Step2: Match congruence criterion

All three pairs of corresponding sides of $\Delta GHJ$ and $\Delta IFJ$ are congruent, which fits the Side-Side-Side (SSS) triangle congruence postulate.

Answer:

SSS