Question

which explains whether \\( \triangle fgh \\) is congruent to \\( \triangle fjh \\)?
they are congruent because \\( \overline { g h } \cong \overline { g f } , \overline { j f } \cong \overline { j h } \\),
and \\( \overline { f h } \cong \overline { f h } \\).
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:

To determine if \(\triangle FGH\) and \(\triangle FJH\) are congruent, we analyze the given diagram and options:

1. Analyze the first option: The sides \( \overline{GH} \cong \overline{GF}\), \( \overline{JF} \cong \overline{JH}\), and \( \overline{FH} \cong \overline{FH}\) (common side). However, this would be SSS, but we need to check if the sides correspond. Wait, actually, looking at the diagram (with markings), \(GF \cong JH\), \(GH \cong JF\), and \(FH\) is common. Wait, no, the second option: The figure seems to be a parallelogram (since opposite sides are marked congruent: \(GF \cong JH\), \(GH \cong JF\)). In a parallelogram, opposite sides are congruent, and the diagonal \(FH\) is common. So by SSS, \(\triangle FGH \cong \triangle FJH\) because \(GF \cong JH\), \(GH \cong JF\), and \(FH \cong FH\). The first option's side correspondences are incorrect. The third and fourth options are wrong because we have three pairs of congruent sides (opposite sides of parallelogram are congruent, plus common side). So the correct reasoning is that they are congruent because opposite sides of a parallelogram are congruent (so \(GF \cong JH\), \(GH \cong JF\)) and \(FH\) is common, satisfying SSS.

Answer:

They are congruent because opposite sides of a parallelogram are congruent. (The option: "They are congruent because opposite sides of a parallelogram are congruent.")