https://file.aiquickdraw.com/mathbot/file/1728512079928hj49taxy.jpg

The two triangles in the image, \(\triangle ABC\) and \(\triangle XYZ\), are similar, which means their corresponding sides are proportional.

The sides of \(\triangle ABC\) are:
- \(AB = 4\)
- \(AC = 6\)

The corresponding sides of \(\triangle XYZ\) are:
- \(XZ = 18\)
- \(XY = ?\) (this is what we need to solve for)

We can set up a proportion using the corresponding sides. The correct proportion would compare \(AB\) with \(XZ\) and \(AC\) with \(XY\). So, the correct setup is:

\[
\frac{AB}{XZ} = \frac{AC}{XY}
\]

Substitute the known values:

\[
\frac{4}{18} = \frac{6}{?}
\]

From the options, this corresponds to the third choice:
\[
\frac{4}{18} = \frac{6}{?}
\]

Let me know if you'd like more details or have questions! 

Here are 5 questions to explore:
1. How do you solve proportions like this one?
2. Why are the triangles similar?
3. How would you calculate the missing side after setting up the proportion?
4. What are the properties of similar triangles?
5. Can this method be applied to non-similar triangles?

**Tip:** When two triangles are similar, all their corresponding angles are equal, and their corresponding sides are proportional.

Which proportion can be used to solve for the missing side in similar triangles ΔABC and ΔXYZ?

Learn how to solve for the missing side in similar triangles ΔABC and ΔXYZ using proportional relationships. The problem involves setting up a proportion based on corresponding sides: AB/XZ = AC/XY. Suitable for students in Grades 7-9.

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