which explains whether (\triangle fgh) is congruent to (\triangle fjh)?\nthey are congruent because…

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

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

Answer

Explanation:

Step1: Analyze the congruence criteria

For two triangles to be congruent, we need to check the congruence of their corresponding sides. The SSS (Side - Side - Side) criterion states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

Step2: Check the given side - congruence statements

In (\triangle FGH) and (\triangle FJH), we are given that (GH\cong GF) is incorrect (from the figure's markings). Also, for the SSS criterion, we need three pairs of congruent sides. If we assume the side - congruence claims in the first option: (GH\cong GF) (incorrect as per the figure's markings, from the figure's tick - marks, we can see the correct side - congruence relationships). The second option about parallelogram is not applicable here as there is no indication that the figure is a parallelogram.

If we consider the side - congruence in the last option: Let's assume the side - congruence from the figure's tick - marks. Suppose (GH = FJ) (one tick), (GF=JH) (two ticks), and (FH) is common. But for SSS, we need three pairs of sides. If we have only two pairs of corresponding sides congruent ((GH = FJ), (GF = JH)) and (FH) is common. But the SSS criterion requires three pairs of sides. If we assume the side - congruence as per the problem's options analysis: The first option has wrong side - congruence ((GH\cong GF) is wrong from the figure's markings). The second option (parallelogram) is not supported by the figure. The third option (only one pair) is wrong as we have two pairs. The fourth option: In (\triangle FGH) and (\triangle FJH), if we assume the side - congruence based on the figure's tick - marks (assuming (GH) and (FJ) have one tick, (GF) and (JH) have two ticks), we have two pairs of corresponding sides congruent. But for triangle congruence (by SSS), we need three pairs. So they are not congruent because only two pairs of corresponding sides are congruent.

Answer:

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