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An illustration shows two pentagons. The pentagon on the left is labeled figure 1, and the pentagon on the right is labeled figure 2. Starting at the bottom left vertex of both figures, the vertices are labeled A, B, C, D, and E. In figure 1, lines connect the vertices A and C and C and E. In figure 2, lines connect the vertices A and D, B and E, and B and D.

Choose the correct decomposition of the regular polygon into n−2 triangles.

(1 point)
Responses

Figure 2 is the correct decomposition because Figure 2 is decomposed into n−2 triangles.
Figure 2 is the correct decomposition because Figure 2 is decomposed into n minus 2 triangles.

Figure 1 is the correct decomposition because Figure 1 is decomposed into n−2=5−2=3 triangles.
Figure 1 is the correct decomposition because Figure 1 is decomposed into n minus 2 equals 5 minus 2 equals 3 triangles.

Figure 1 is the correct decomposition because Figure 1 is decomposed into triangles that are equal sizes.
Figure 1 is the correct decomposition because Figure 1 is decomposed into triangles that are equal sizes.

Figure 2 is the correct decomposition because Figure 2 is decomposed into 5 triangles.
Figure 2 is the correct decomposition because Figure 2 is decomposed into 5 triangles.
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1 answer

To determine the correct decomposition of a pentagon (which is a polygon with 5 sides) into triangles, we can use the formula \( n - 2 \), where \( n \) is the number of sides of the polygon. In this case, since we have a pentagon, \( n = 5 \):

\[ n - 2 = 5 - 2 = 3 \]

This means that a pentagon can be decomposed into 3 triangles.

To analyze the provided options based on the decomposition shown in the figures:

  • Figure 1: If it correctly connects the vertices to form 3 triangles, then it is a valid decomposition.
  • Figure 2: If it connects the vertices in such a way that it creates more than 3 triangles, then it is not a valid decomposition.

Since we need to establish whether figure 1 or figure 2 correctly corresponds to the decomposition of a pentagon into \( n - 2 \) triangles:

  • Figure 1 is the correct decomposition because Figure 1 is decomposed into \( n - 2 = 5 - 2 = 3 \) triangles.

The correct response is:

Figure 1 is the correct decomposition because Figure 1 is decomposed into n−2=5−2=3 triangles.