Question

which explains whether △fgh is congruent to △fjh? they are congruent because (overline{gh}congoverline{gf}), (overline{jf}congoverline{jh}), and (overline{fh}congoverline{fh}). they are congruent because opposite sides of a parallelogram are congruent. they are not congruent because only one pair of corresponding sides is congruent. they are not congruent because only two pairs of corresponding sides are congruent.

Explanation:

Step1: Recall congruence criteria

For two triangles to be congruent, we need all corresponding sides and angles to be congruent. In triangles $\triangle FGH$ and $\triangle FJH$, we are given some side - equalities.

Step2: Analyze given side - equalities

We have $\overline{GH}\cong\overline{GF}$, $\overline{JF}\cong\overline{JH}$, and $\overline{FH}=\overline{FH}$ (reflexive property). By SSS (Side - Side - Side) congruence criterion, if three pairs of corresponding sides of two triangles are congruent, the triangles are congruent.

Answer:

They are congruent because $\overline{GH}\cong\overline{GF}$, $\overline{JF}\cong\overline{JH}$, and $\overline{FH}\cong\overline{FH}$.