To determine the correct decomposition of the polygons based on the provided options, we need to analyze the decompositions of both figures:
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Understanding Decomposition: For a polygon with \( n \) sides, it can be decomposed into \( n-2 \) triangles. For a pentagon (5-sided polygon), this means it can be decomposed into \( 5 - 2 = 3 \) triangles.
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Analyzing Figure 1: The description states that lines connect points A to C and C to E. If this results in 3 triangles, then it satisfies the condition of a correct decomposition for a pentagon.
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Analyzing Figure 2: The lines connecting A to D, B to E, and B to D suggest a different arrangement. If this results in 5 triangles, then this would be more than \( n - 2 \) for a pentagon.
Now, let's evaluate the options based on this understanding:
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Figure 1 is the correct decomposition because Figure 1 is decomposed into triangles that are equal sizes.
- This is incorrect because equal size is not a necessary condition for decomposition; it just needs to be \( n - 2 \) triangles.
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Figure 2 is the correct decomposition because Figure 2 is decomposed into 5 triangles.
- This is incorrect; it needs to have \( n - 2 = 3 \) triangles, not 5.
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Figure 1 is the correct decomposition because Figure 1 is decomposed into \( n-2=5-2=3 \) triangles.
- This is correct; it properly reflects the requirement.
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Figure 2 is the correct decomposition because Figure 2 is decomposed into \( n-2 \) triangles.
- This is incorrect; as explained, it decomposed into more than \( n - 2 \) triangles.
The best response based on the analysis is:
Figure 1 is the correct decomposition because Figure 1 is decomposed into \( n-2=5-2=3 \) triangles.