To determine which combination of figures is similar, we need to analyze the shapes of the rectangles and their properties, such as side lengths and angles.
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Figure 1 is a rectangle that covers the 2nd row in the 3rd through 6th columns, giving it a dimension of 1 row by 4 columns. Thus, its side lengths are 1 (height) and 4 (width).
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Figure 2 spans from the 2nd to the 9th rows in the 9th and 10th columns, resulting in a dimension of 8 rows by 2 columns. Its side lengths are 8 (height) and 2 (width).
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Figure 3 covers the 4th to the 7th rows in the 4th and 5th columns, leading to a dimension of 4 rows by 2 columns. Its side lengths are 4 (height) and 2 (width).
Now let's check the similarity based on the definitions:
- For two rectangles to be similar, their corresponding side lengths should be proportional, and their angles should be equal (which they are inherently for rectangles).
Let's calculate the ratios of the sides:
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Figure 1:
- Height: 1
- Width: 4
- Ratio (Height/Width) = 1/4
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Figure 2:
- Height: 8
- Width: 2
- Ratio (Height/Width) = 8/2 = 4 (which simplifies to 2)
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Figure 3:
- Height: 4
- Width: 2
- Ratio (Height/Width) = 4/2 = 2
Now we can analyze the combinations:
- Figure 1 and Figure 2: They have different proportions (1/4 and 4), so they are not similar.
- Figure 1, Figure 2, and Figure 3: They do not share the same properties proportionality-wise; thus, they are not similar.
- Figure 1 and Figure 3: They have a height to width ratio of 1/4 and 2, respectively, so they are not similar.
- Figure 2 and Figure 3: They have ratios of 4 and 2, which means they are not similar.
The only property shared among Figures 1, 2, and 3 is that they are rectangles. Therefore, the conclusion is:
Figure 1, Figure 2, and Figure 3; all figures are rectangles.