Similar Triangles: Identify Matching Pairs and Calculate Their Ratio

To solve this problem, we'll compare the side ratios of the given triangles to determine which pair are similar and find the similarity ratio.

• Step 1: Identify the given triangle side lengths:
  Triangle A: Sides of length $8$, $4$, and $6$.
  Triangle B: Sides of length $10$, $6$, and $8$.
  Triangle C: Sides of length $4$, $2$, and $3$.
• Step 2: Compare the ratios of corresponding sides between pairs of triangles.

Comparing Triangle A and Triangle B:

• Ratio $\frac{8}{10} = 0.8$; $\frac{4}{6} \approx 0.67$; $\frac{6}{8} = 0.75$

Here, the ratios are not equal; hence, triangles A and B are not similar.

Comparing Triangle A and Triangle C:

• Ratio $\frac{8}{4} = 2$; $\frac{4}{2} = 2$; $\frac{6}{3} = 2$

All ratios are equal, so triangles A and C are similar, with a similarity ratio of 2.

Comparing Triangle B and Triangle C:

• Ratio $\frac{10}{4} = 2.5$; $\frac{6}{2} = 3$; $\frac{8}{3} \approx 2.67$

The ratios are not equal, so triangles B and C are not similar.

Therefore, the similar triangles are Triangle A and Triangle C, with a similarity ratio of 2.

The correct answer is A + C are similar with a ratio of 2.