Question

which explains whether \\( \triangle fgh \\) is congruent to \\( \triangle fjh \\)?
\\( \bigcirc \\) 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 } \\)
\\( \bigcirc \\) they are congruent because opposite sides of a
parallelogram are congruent
\\( \bigcirc \\) they are not congruent because only one pair of
corresponding sides is congruent
\\( \bigcirc \\) they are not congruent because only two pairs of
corresponding sides are congruent

Explanation:

Step1: Analyze the first option

The first option claims \( \overline{GH}\cong\overline{GF}\), \( \overline{JF}\cong\overline{JH}\), and \( \overline{FH}\cong\overline{FH}\). But from the figure, there is no indication that \( \overline{GH}\cong\overline{GF}\) or \( \overline{JF}\cong\overline{JH}\).

Step2: Analyze the second option

The second option says they are congruent because opposite sides of a parallelogram are congruent. But the figure is not a parallelogram (a parallelogram has two pairs of parallel sides, which is not indicated here).

Step3: Analyze the third option

The third option says only one pair of corresponding sides is congruent. But from the figure, we can see two pairs of sides (\(GF = JH\) and \(GH=JF\)) are congruent. So this is incorrect.

Step4: Analyze the fourth option

For triangle congruence (like SSS - three sides, SAS - two sides and included angle etc.), here we have two pairs of sides congruent (\(GF = JH\), \(GH = JF\)) and a common side \(FH\). But we don't have the included angle or the third side to satisfy a congruence criterion (e.g., SSS or SAS). So the two triangles \( \triangle FGH\) and \( \triangle FJH\) are not congruent as only two pairs of corresponding sides are congruent.

Answer:

They are not congruent because only two pairs of corresponding sides are congruent