https://file.aiquickdraw.com/mathbot/file/1726098080134i49e6zyg.jpg

To determine whether the two quadrilaterals in the image are similar, we need to check if the corresponding angles are equal and if the sides are proportional.

### Step 1: Compare Corresponding Angles
Both shapes have the angles marked in red, and it appears that the corresponding angles are congruent based on the markings. For similarity, equal angles in corresponding positions is a key requirement, so this criterion seems satisfied.

### Step 2: Check the Proportions of Corresponding Sides
Next, we check if the sides are proportional. Let's label the corresponding sides:

- In the first quadrilateral \(ONMP\):
  - \(ON = 28 \, \text{km}\)
  - \(NM = 24 \, \text{km}\)
  - \(MP = 28 \, \text{km}\)
  - \(OP = 49 \, \text{km}\)

- In the second quadrilateral \(SVTU\):
  - \(SV = 20 \, \text{km}\)
  - \(VT = 49 \, \text{km}\)
  - \(TU = 20 \, \text{km}\)
  - \(SU = 31 \, \text{km}\)

Now we calculate the ratios of corresponding sides:

- \( \frac{ON}{SV} = \frac{28}{20} = 1.4 \)
- \( \frac{NM}{VT} = \frac{24}{49} \approx 0.49 \)
- \( \frac{MP}{TU} = \frac{28}{20} = 1.4 \)
- \( \frac{OP}{SU} = \frac{49}{31} \approx 1.58 \)

### Step 3: Conclusion
For two shapes to be similar, the ratio of all corresponding sides must be the same. Here, the side ratios are:

- \( 1.4 \)
- \( 0.49 \)
- \( 1.4 \)
- \( 1.58 \)

Since the ratios of corresponding sides are not consistent, the two quadrilaterals are **not similar**.

Would you like a detailed explanation of a particular part of the solution or further clarification? 

Here are 5 related questions to expand your understanding:
1. What are the properties of similar shapes?
2. How do we prove the similarity of triangles?
3. What is the significance of corresponding angles in similarity?
4. How do we find the scale factor in similar polygons?
5. What are the different types of quadrilaterals and their properties?

**Tip**: Always check both angles and side ratios when determining the similarity of polygons.

Learn how to determine if two quadrilaterals are similar by comparing their corresponding angles and side ratios. Understand the application of the Angle-Angle Similarity Theorem and Side-Side-Side Similarity Theorem, suitable for students in Grades 8-10.

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