I can help analyze the uploaded worksheet and solve the problems. Here is what I see:

Problem 1

The question asks to verify if triangles $\triangle ABC$ and $\triangle FGH$ are similar. This involves checking if their corresponding sides are proportional and/or their corresponding angles are equal.

Steps:

1. Check side ratios:

   • $\frac{AB}{FH} = \frac{72}{14} = 5.14$
   • $\frac{AC}{FG} = \frac{84}{12} = 7$
   • $\frac{BC}{GH} = \frac{48}{8} = 6$

   These ratios are not equal, so the triangles are not similar.

2. Check angles if needed (not visible on the page).

Conclusion: The triangles $\triangle ABC$ and $\triangle FGH$ are not similar.

Problem 2

The triangles $\triangle JKL$ and $\triangle MNO$ are similar, and the task is to find the missing side lengths.

Given:

• $JK = 10$, $JL = 8$, $KL = ?$
• $MN = 18$, $MO = 12$, $NO = ?$

Solution Steps:

1. Use the similarity ratio: $\text{Scale factor} = \frac{MN}{JK} = \frac{18}{10} = 1.8$

2. Find $KL$ (corresponding to $NO$): $KL = NO = \frac{JL}{1.8} = \frac{8}{1.8} \approx 4.44 \, \text{m}.$

Let me know if you'd like detailed calculations! Now here are some related questions and tips.

Follow-up Questions:

1. What are other methods to prove triangle similarity?
2. How do we find missing angles in similar triangles?
3. Why do proportional sides guarantee similarity?
4. Can the similarity principle apply to real-world scenarios (e.g., shadows)?
5. How do we confirm if two triangles are congruent instead of similar?

Tip:

Always double-check the corresponding sides and angles when comparing two triangles for similarity or congruence! Misalignment can lead to incorrect ratios.