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 SSS (Side - Side - Side), SAS (Side - Angle - Side), ASA (Angle - Side - Angle), AAS (Angle - Angle - Side) or HL (Hypotenuse - Leg for right - triangles). Here, we are looking at side - side - side relationships.

Step2: Analyze given side - equalities

In \(\triangle FGH\) and \(\triangle FJH\), we are not given that \(\overline{GH}\cong\overline{GF}\), \(\overline{JF}\cong\overline{JH}\), and \(\overline{FH}\cong\overline{FH}\) is not enough for congruence. Also, just because opposite sides of a parallelogram are congruent doesn't mean these two triangles are congruent. We need all three pairs of corresponding sides to be congruent for SSS. Since we don't have that, they are not congruent because only two pairs of corresponding sides are congruent is a correct statement.

Answer:

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