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To determine if it is possible to draw a polygon that is a scaled copy of both Polygon A and Polygon B, we need to analyze their proportions and structure.

1. **Step 1: Check Shape Similarity**
   First, we need to see if the shapes are similar. This means checking if Polygon A and Polygon B have the same overall shape but possibly different sizes.

   - Polygon A appears to have a step-like structure, with 5 horizontal sections and 2 vertical connections. We can count the number of units along both the x- and y-axes to define its overall dimensions.
   - Polygon B also has a step-like structure but seems elongated compared to Polygon A. We need to check its dimensions similarly.

2. **Step 2: Compare Proportions**
   If the shapes are proportionally similar, we can check if one is a scaled version of the other. A scaled polygon will have all corresponding sides proportional. The scale factor should be constant across all corresponding sides.

3. **Step 3: Calculate and Compare Scale Factors**
   Let's count the grid units for both shapes:
   - Polygon A: The base is 5 units, and the height is 2 units.
   - Polygon B: The base is 10 units, and the height is 4 units.
   
   The ratio of the base of Polygon B to Polygon A is \( \frac{10}{5} = 2 \), and the ratio of the height is \( \frac{4}{2} = 2 \). Since both the base and the height have the same scale factor of 2, Polygon B is a scaled copy of Polygon A by a factor of 2.

4. **Conclusion**
   Since Polygon B is a scaled copy of Polygon A with a scale factor of 2, it is possible to draw a polygon that is a scaled version of both polygons. In fact, Polygon B already represents this scaled polygon.

Would you like further details or have any specific questions?

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Here are 5 related questions to explore further:
1. What is a general method to identify if two polygons are similar?
2. How do we calculate scale factors between two geometric shapes?
3. What are the key properties of similar polygons?
4. Can any polygon be scaled by an arbitrary factor and still maintain similarity?
5. What are some practical applications of scaling in geometry?

**Tip**: When checking for similarity between polygons, always compare the ratios of corresponding sides and angles!

Is it possible to draw a polygon that is a scaled copy of both Polygon A and Polygon B?

Explore whether it is possible to draw a polygon that is a scaled copy of both Polygon A and Polygon B. Learn about the concept of polygon similarity, scaling factors, and the necessary conditions for two shapes to be scaled copies. Suitable for students in Grades 8-10.

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