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We are given that quadrilateral EFGH is similar to quadrilateral IJKL. Since they are similar, the corresponding sides of the two quadrilaterals are proportional.

The sides provided in the image are as follows:
- EF corresponds to IJ (but the value of EF is not provided),
- FG corresponds to JK (we need to find JK),
- GH corresponds to KL (GH = 41, KL = 20),
- HE corresponds to LI (but the value of HE is not provided).

We can use the proportionality of the corresponding sides to find the missing side, JK.

The ratio of the corresponding sides is given by:

\[
\frac{GH}{KL} = \frac{FG}{JK}
\]

Substitute the known values into this equation:

\[
\frac{41}{20} = \frac{29}{JK}
\]

Now, we solve for \( JK \):

\[
JK = \frac{29 \times 20}{41}
\]

Let's compute the value of \( JK \).The length of side \( JK \) is approximately 14.1 (rounded to the nearest tenth).

Would you like more details on the solution or have any questions?

Here are 5 related questions to extend your understanding:
1. How would you solve if the ratio of the sides wasn't directly given?
2. How do you verify that two polygons are similar?
3. What happens to the angles when two quadrilaterals are similar?
4. How does the area ratio of two similar polygons relate to the side ratio?
5. What are the implications of similarity in 3D shapes?

**Tip:** Always ensure you set up proportions correctly when dealing with similar shapes to avoid confusion with corresponding sides.

Quadrilateral EFGH is similar to quadrilateral IJKL. Find the measure of side JK. Round your answer to the nearest tenth if necessary.

Learn how to solve for the length of side JK in quadrilateral IJKL, given that it is similar to quadrilateral EFGH. This solution involves setting up and solving proportions between corresponding sides of the similar shapes. Ideal for students in Grades 8-10.

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