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The problem asks to calculate the similarity ratio (or scale factor) \( k \) between two similar triangles \( \triangle ABC \) and \( \triangle DEF \).

### Given dataThe problem asks to calculate the similarity ratio (or scale factor) \( k \) between two similar triangles \( \triangle ABC \) and \( \triangle DEF \).

### Given 
- \( AB = BC = 99 \, \text{cm} \), \( AC = 126 \, \text{cm} \)
- \( DE = EF = 11 \, \text{cm} \), \( DF = 14 \, \text{cm} \)

### To solve:
For similar triangles, the ratio of corresponding sides is the same, so the similarity coefficient \( k \) can be calculated using any pair of corresponding sides. Let's choose the sides \( AB \) and \( DE \).

\[
k = \frac{AB}{DE} = \frac{99}{11} = 9
\]

Thus, the similarity coefficient \( k = 9 \).

Would you like more details on this or have any questions?

Here are 5 related questions you might find interesting:
1. How do you confirm that two triangles are similar?
2. What other ratios could be used to find \( k \)?
3. How does the area ratio between similar triangles relate to the similarity coefficient?
4. If the triangles were reversed, what would happen to the value of \( k \)?
5. How can we use the angles of the triangles to further verify similarity?

**Tip:** When working with similar triangles, always ensure that you compare corresponding sides correctly to avoid errors.

Given that triangles ABC and DEF are similar, with the side lengths AB = BC = 99 cm, AC = 126 cm, DE = EF = 11 cm, and DF = 14 cm, calculate the similarity coefficient k.

Calculate the similarity coefficient (k) for triangles ABC and DEF with given side lengths: AB = 99 cm, BC = 99 cm, AC = 126 cm, DE = 11 cm, EF = 11 cm, and DF = 14 cm. A step-by-step solution using the properties of similar triangles and corresponding side ratios.

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