Question

Use the image to answer the question. Choose the correct decomposition of the polygon into n−2 triangles. (1 point) Responses Figure 2 is the correct decomposition because it has n−2=4−2=2 triangles. Figure 2 is the correct decomposition because it has n minus 2 equals 4 minus 2 equals 2 triangles. Figure 1 is the correct decomposition because it has 4 triangles of the equal size. Figure 1 is the correct decomposition because it has 4 triangles of the equal size. Figure 1 is the correct decomposition because Figure 1 is decomposed into 2 triangles that are equal sizes. Figure 1 is the correct decomposition because Figure 1 is decomposed into 2 triangles that are equal sizes. Figure 1 is the correct decomposition because Figure 1 is decomposed into 4 triangles that are not equal sizes. Figure 1 is the correct decomposition because Figure 1 is decomposed into 4 triangles that are not equal sizes. Skip to navigation

Answer 1

To determine the correct decomposition of a polygon into \( n-2 \) triangles, we need to clarify what \( n \) represents. Here, \( n \) usually refers to the number of vertices in the polygon.

If the polygon has 4 vertices (which is typical for a quadrilateral), then the calculation for the number of triangles into which it can be decomposed is:

\[ n - 2 = 4 - 2 = 2 \]

This means that the polygon should be decomposed into exactly 2 triangles.

From the provided options, the correct answer will mention that the decomposition should result in 2 triangles. Thus:

• "Figure 2 is the correct decomposition because it has \( n - 2 = 4 - 2 = 2 \) triangles."

is the correct statement because it aligns with the requirement of creating \( n - 2 \) triangles from a polygon with 4 vertices.

If you have visual representations to consult, the confirmation should ideally come from verifying which figure indeed contains the correct number of triangles as mentioned above.