To solve this, we must verify the similarity statements and corresponding similarity theorems for the given triangles.

Triangle $ABC$ and $DEF$:

• Corresponding sides are proportional:
  • $AB / DE = 3 / 4.5 = 2 / 3$,
  • $BC / EF = 2 / 3 = 2 / 3$,
  • $AC / DF = 3.5 / 5.25 = 2 / 3$.

Since all sides are proportional (in the same ratio $2:3$), $\triangle ABC \sim \triangle DEF$ by the SSS Similarity Theorem.

Triangle $ABC$ and $GHI$:

• Two sides and the included angles match:
  • $AB / GH = 3 / 6 = 1 / 2$,
  • $AC / GI = 3.5 / 7 = 1 / 2$,
  • The included angle $\angle A$ and $\angle G$ are congruent.

Since two sides are proportional and the included angles are equal, $\triangle ABC \sim \triangle GHI$ by the SAS Similarity Theorem.

Final Answers:

1. $\triangle ABC \sim \triangle DEF$ by the SSS Similarity Theorem.
2. $\triangle ABC \sim \triangle GHI$ by the SAS Similarity Theorem.

Would you like a detailed breakdown of the ratios or angles used in each similarity theorem?

Related Questions:

1. What are the conditions for the SAS Similarity Theorem?
2. How do you verify similarity using the SSS Similarity Theorem?
3. Why are proportional sides important for triangle similarity?
4. How can you determine congruent angles in triangles?
5. How do you write a similarity statement for triangles?

Tip:

Always check all sides and angles carefully when applying similarity theorems to avoid errors in proportionality.