which explains whether △fgh is congruent to △fjh? they are not congruent because only one pair of corresponding sides is congruent. they are congruent because opposite sides of a parallelogram are congruent. they are congruent because $\overline{gh} \cong \overline{gf}$, $\overline{jf} \cong \overline{jh}$, and $\overline{fh} \cong \overline{fh}$ they are not congruent because only two pairs of corresponding sides are congruent.

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# Explanation:
## Step1: Analyze the figure
From the diagram, we can see that $ GF \cong JH $ (single tick marks), $ JF \cong JH $? Wait, no, $ JF $ and $ JH $ have double tick marks? Wait, looking at the figure: $ GF $ and $ JH $ have single tick marks (so $ GF \cong JH $), $ JF $ and $ JH $? Wait, no, $ JF $ and $ JH $? Wait, the sides $ JF $ and $ JH $? Wait, actually, $ JF $ and $ JH $ – no, looking at the figure, $ JF $ and $ JH $? Wait, the quadrilateral: $ FJ $ and $ JH $? Wait, no, the triangles are $ \triangle FGH $ and $ \triangle FJH $. Let's check the sides:

- $ GF \cong JH $ (single tick marks)
- $ JF \cong JH $? Wait, no, $ JF $ and $ JH $ – wait, $ JF $ and $ JH $ have double tick marks? Wait, the side $ FJ $ and $ JH $? Wait, no, the side $ FJ $ and $ JH $ – actually, $ FJ $ and $ JH $ – wait, the common side is $ FH $. So for $ \triangle FGH $ and $ \triangle FJH $:

- $ GF \cong JH $ (given by single tick)
- $ JF \cong GH $? Wait, no, the double tick marks: $ FJ $ and $ JH $? Wait, no, the double tick marks are on $ FJ $ and $ JH $? Wait, the figure: $ FJ $ has double tick, $ JH $ has double tick? Wait, no, the side $ FJ $ and $ JH $ – wait, the quadrilateral: $ FJ $ and $ JH $ are equal (double tick), $ GF $ and $ JH $ – no, $ GF $ and $ GH $? Wait, maybe I misread. Let's re-examine:

The triangles are $ \triangle FGH $ and $ \triangle FJH $. Let's list the sides:

- $ GF $ and $ JH $: single tick, so $ GF \cong JH $
- $ FJ $ and $ GH $: wait, no, $ FJ $ has double tick, $ JH $ has double tick? Wait, the side $ FJ $ and $ JH $ – no, the side $ FJ $ and $ JH $ are equal (double tick), and $ GF $ and $ GH $ – no, $ GF $ has single tick, $ GH $ has single tick? Wait, no, the single tick is on $ GF $ and $ GH $? Wait, no, the figure: $ GF $ (top side) has single tick, $ GH $ (right side) has single tick? No, the right side $ GH $ has single tick, top side $ GF $ has single tick? Wait, no, the left side $ FJ $ has double tick, bottom side $ JH $ has double tick. So:

For $ \triangle FGH $ and $ \triangle FJH $:

- $ GF \cong JH $ (single tick)
- $ JF \cong GH $ (double tick? Wait, no, $ FJ $ and $ GH $ – no, $ FJ $ has double tick, $ GH $ has single tick? Wait, I think I made a mistake. Let's look at the third option: "They are congruent because $ \overline{GH} \cong \overline{GF} $, $ \overline{JF} \cong \overline{JH} $, and $ \overline{FH} \cong \overline{FH} $". Wait, no, the third option says $ \overline{GH} \cong \overline{GF} $, $ \overline{JF} \cong \overline{JH} $, and $ \overline{FH} \cong \overline{FH} $. Wait, but that would be SSS? Wait, no, $ \overline{GH} \cong \overline{GF} $ – is that true? Wait, the single tick marks: $ GF $ and $ GH $ – no, the single tick is on $ GF $ and $ JH $. Wait, maybe the correct approach is:

The triangles $ \triangle FGH $ and $ \triangle FJH $:

- $ GF \cong JH $ (single tick)
- $ JF \cong GH $ (double tick? Wait, no, $ FJ $ and $ GH $ – no, $ FJ $ has double tick, $ JH $ has double tick. Wait, the common side is $ FH $, so $ FH \cong FH $ (reflexive property). So if we have:

- $ GF \cong JH $
- $ JF \cong GH $
- $ FH \cong FH $

Then by SSS, the triangles are congruent. Wait, but the third option says $ \overline{GH} \cong \overline{GF} $, $ \overline{JF} \cong \overline{JH} $, and $ \overline{FH} \cong \overline{FH} $. Wait, maybe that's a typo, but let's check the options:

Option 3: "They are congruent because $ \overline{GH} \cong \overline{GF} $, $ \overline{JF} \cong \overline{JH} $, and $ \overline{FH} \cong \overline{FH} $". Wait, no, maybe it's $ \overline{GF} \cong \overline{JH} $, $ \overline{JF} \cong \overline{GH} $, and $ \overline{FH} \cong \overline{FH} $. But the option says $ \overline{GH} \cong \overline{GF} $, $ \overline{JF} \cong \overline{JH} $, and $ \overline{FH} \cong \overline{FH} $. Wait, maybe the correct reasoning is that the triangles have three congruent sides: $ GF \cong JH $, $ JF \cong GH $, and $ FH \cong FH $, so by SSS, they are congruent. So the third option (the one with $ \overline{GH} \cong \overline{GF} $, $ \overline{JF} \cong \overline{JH} $, and $ \overline{FH} \cong \overline{FH} $) is the correct one, because it's using SSS: two sides from the tick marks and the common side.

Wait, but let's check the other options:

- Option 1: "They are congruent because opposite sides of a parallelogram are congruent." But we are dealing with triangles, not parallelogram sides directly.
- Option 2: "They are not congruent because only one pair of corresponding sides is congruent." But we have more than one.
- Option 4: "They are not congruent because only two pairs of corresponding sides are congruent." But we have three (with the common side).

So the correct option is the third one: "They are congruent because $ \overline{GH} \cong \overline{GF} $, $ \overline{JF} \cong \overline{JH} $, and $ \overline{FH} \cong \overline{FH} $". Wait, maybe the notation is off, but the key is SSS: two sides from the tick marks and the common side. So the third option (the bottom-left one) is correct.

## Step2: Identify the correct option
The third option (the one with $ \overline{GH} \cong \overline{GF} $, $ \overline{JF} \cong \overline{JH} $, and $ \overline{FH} \cong \overline{FH} $) explains that the triangles are congruent by SSS (three congruent sides: two from the tick marks and the common side $ FH $).

# Answer:
The third option (bottom - left) which states "They are congruent because $ \overline{GH} \cong \overline{GF} $, $ \overline{JF} \cong \overline{JH} $, and $ \overline{FH} \cong \overline{FH} $".

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