To determine the correct decomposition of the polygon (which is a square in this case) into \( n-2 \) triangles, we first need to know that in a polygon with \( n \) vertices, the number of triangles obtained through triangulation is \( n-2 \).
Given that the polygon has 4 vertices (A, B, C, D), we can substitute \( n = 4 \) into \( n-2 \):
\[ n - 2 = 4 - 2 = 2 \]
This means the polygon can be decomposed into 2 triangles.
Analyzing the Figures:
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Figure 1: If Figure 1 is showing the polygon decomposed into 4 triangles, that would not satisfy the requirement of \( n-2 \) for a square. Although it could show equal-sized triangles, it is still incorrect since we only need 2 triangles.
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Figure 2: If Figure 2 connects vertices B and D (and possibly forms the other necessary line to complete the triangles), and indeed it results in 2 triangles, then it would satisfy \( n-2 \) since 4 vertices yield 2 triangles.
Conclusion:
Therefore, the correct response is:
Figure 2 is the correct decomposition because it has \( n-2 = 4-2 = 2 \) triangles.