Question

which explains whether (\triangle fgh) is congruent to (\triangle 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:

• For the first option: In \(\triangle FGH\) and \(\triangle FJH\), we know that \(GH

ot\cong GF\) (from the markings in the figure, \(GH\) and \(FJ\) are marked as equal, \(GF\) and \(JH\) are not marked as equal in the way described in the first - option). Also, \(JF
ot\cong JH\) (the markings show \(JF = FH\) in a different sense).

• For the second option: There is no indication that the figure is a parallelogram. A parallelogram has two pairs of opposite sides parallel, and we have no information about parallel sides from the given congruence markings.
• For the third option: From the figure, we have \(GH\cong FJ\), \(GF\cong JH\), and \(FH\) is common (\(FH\cong FH\)). So, the statement “only one pair of corresponding sides is congruent” is wrong.
• For the fourth option: In \(\triangle FGH\) and \(\triangle FJH\), we have \(GH\cong FJ\), \(GF\cong JH\), and \(FH\) is a common side (\(FH\cong FH\)). But for triangle congruence (by SSS - Side - Side - Side criterion, we need three pairs of corresponding sides to be congruent). Here, we have only two pairs of non - common corresponding sides (\(GH\cong FJ\), \(GF\cong JH\)) and one common side (\(FH\)). The two triangles do not satisfy the SSS criterion for congruence.

Answer:

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