To determine the correct decomposition of a regular polygon into \(n - 2\) triangles, we first need to understand that for an \(n\)-sided polygon, it can be decomposed into \(n - 2\) triangles when drawn from one vertex to all non-adjacent vertices.
Given that \(n\) is 5 (which indicates a pentagon), we have:
\[ n - 2 = 5 - 2 = 3 \]
This means a correct decomposition of the pentagon would involve creating 3 triangles.
Now we evaluate the options:
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Figure 2 is the correct decomposition because Figure 2 is decomposed into n−2 triangles.
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Figure 2 is the correct decomposition because Figure 2 is decomposed into n minus 2 triangles.
These options are true but need to specify the exact number of triangles to be valid.
- Figure 1 is the correct decomposition because Figure 1 is decomposed into triangles that are equal sizes.
This describes the equal size of the triangles but does not ensure that the count is \(n - 2\).
- Figure 1 is the correct decomposition because Figure 1 is decomposed into n−2=5−2=3 triangles.
This correctly identifies the number of triangles formed.
- Figure 1 is the correct decomposition because Figure 1 is decomposed into n minus 2 equals 5 minus 2 equals 3 triangles.
Again, this correctly identifies the number of triangles formed.
- Figure 2 is the correct decomposition because Figure 2 is decomposed into 5 triangles.
This is incorrect, as a pentagon should only decompose into 3 triangles.
The most accurate responses would be the ones that accurately reflect the number of triangles formed. Therefore, the best answer is:
Figure 1 is the correct decomposition because Figure 1 is decomposed into n−2=5−2=3 triangles.
1 answer