The task in the image requires verifying whether the triangles $\triangle ABC$ and $\triangle FGH$ are similar by comparing their corresponding sides' proportions. Here's the step-by-step breakdown:

Step 1: Corresponding sides

From the diagram:

• $AB = 72, AC = 84, BC = 48$ for $\triangle ABC$.
• $FH = 14, FG = 12, GH = 8$ for $\triangle FGH$.

Step 2: Calculate the ratios of corresponding sides

We check if the ratios of all corresponding sides are equal:

1. $\frac{AB}{FH} = \frac{72}{14}$
2. $\frac{AC}{FG} = \frac{84}{12}$
3. $\frac{BC}{GH} = \frac{48}{8}$

Perform the calculations:

1. $\frac{72}{14} = 5.14$ (approx.)
2. ( \frac{84}{14Let’s complete the solution step-by-step:

Step 2: Calculate the ratios of corresponding sides (continued)

1. $\frac{AB}{FH} = \frac{72}{14} = 5.14$ (approx.)
2. $\frac{AC}{FG} = \frac{84}{12} = 7$
3. $\frac{BC}{GH} = \frac{48}{8} = 6$

Clearly, these ratios are not equal, which means that $\triangle ABC$ and $\triangle FGH$ are not similar.

Conclusion:

The triangles are not similar because the corresponding side ratios are not proportional.

Do you have any further questions or want me to explain another aspect in more detail? Let me know! 😊

Here are 5 questions related to this topic you might want to explore:

1. What is the definition of similar triangles, and what properties must they satisfy?
2. How can we determine if two triangles are similar using their angles instead of sides?
3. Why is proportionality crucial for proving similarity?
4. Can triangles with the same area be considered similar? Why or why not?
5. How can the similarity of triangles be applied in solving real-world problems?

Tip: Always verify all corresponding side ratios (or angles) to ensure your similarity claim is accurate!