https://file.aiquickdraw.com/mathbot/file/1730815873333p1wo44bl.jpg

Let's go through each of the problems in this image.

### First Problem
For the first triangle pair, we have:
1. Triangle \( \triangle ABC \) with sides \( AC = x \), \( AB = 25 \), and the other triangle \( \triangle XYZ \) with sides \( XZ = 6 \) and \( XY = 10 \).
  
Since the triangles are similar, we can set up a proportion using corresponding sides:
\[
\frac{AC}{XZ} = \frac{AB}{XY}
\]
Substitute the known values:
\[
\frac{x}{6} = \frac{25}{10}
\]
Now, cross-multiply and solve for \( x \):
\[
10x = 6 \times 25
\]
\[
10x = 150
\]
\[
x = 15
\]

So, \( AC = 15 \).

### Second Problem
In the second triangle pair, we have:
1. Triangle \( \triangle ABC \) with sides \( AB = 50 \), \( BC = 40 \), and the other triangle \( \triangle YZX \) with sides \( YZ = 20 \) and \( ZX = x \).
  
Using the similarity property again:
\[
\frac{BC}{YZ} = \frac{AB}{YX}
\]
Substitute the known values:
\

Given the figures are similar, find the missing side in each pair of triangles and quadrilaterals shown in the image.

Explore how to find missing sides in similar figures using proportions. This solution covers similarity of triangles, ratio concepts, and the Proportionality Theorem. Suitable for Grades 8-10, this problem helps students learn essential concepts in geometry with detailed examples.

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