The problem involves establishing a proportion between similar triangles. Let’s analyze the given triangles and their corresponding sides:

1. Given: Triangles $\triangle DBC$ and $\triangle EFG$ are shown. The problem asks to fill in the appropriate side lengths to complete the proportion $\frac{EF}{BC} = \frac{\text{?}}{\text{?}}$.

2. Key Property: Similar triangles have corresponding sides in proportion. The angles marked in the triangles indicate similarity, so we need to match corresponding sides.

Corresponding Sides:

• $EF$ corresponds to $BC$ (as they are the same relative sides in the similar triangles).
• $FG$ corresponds to $CD$, and $EG$ corresponds to $DB$.

Proportion:

The proportion can be filled as follows: $\frac{EF}{BC} = \frac{EG}{DB}.$

So, you would fill the blanks with:

• Numerator of the second fraction: $EG$,
• Denominator of the second fraction: $DB$.

Would you like further clarification on triangle similarity or proportions? Let me know!

Related Questions:

1. How can we determine if two triangles are similar?
2. What are the properties of corresponding sides in similar triangles?
3. How can angle similarity help in solving for proportions?
4. What other methods could be used to verify proportionality in triangles?
5. Can this method be applied to real-world problems involving scaling?

Tip:

Always identify corresponding sides by comparing the positions of angles and matching sides in the given triangles.