Use the image to answer the question. Choose the correct decomposition of the regular polygon into n−2 triangles. (1 point) Responses 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 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 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 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. Skip to navigation

Answer 1

To determine the correct decomposition of a regular polygon into \(n-2\) triangles, we need to recall that a polygon with \(n\) sides can be divided into \(n-2\) triangles by drawing non-crossing diagonals from one vertex to the other non-adjacent vertices.

Given that:

• \(n = 5\) (the polygon is a pentagon),
• \(n-2 = 5-2 = 3\),

we should look for the decomposition that shows a pentagon divided into exactly 3 triangles.

• If Figure 1 shows 3 triangles (the correct number) that could be formed by drawing diagonals from one vertex to other non-adjacent vertices, then Figure 1 is correct.
• If Figure 2 shows more than 3 triangles (like 5 triangles), then it is incorrect as per the \(n-2\) rule for a pentagon.

Without the images, I cannot definitively determine which figure is the correct decomposition, but the answer will be identified by:

1. Check if it decomposes into exactly 3 triangles (for a pentagon).
2. Ensure the decomposition is valid and does not cross any diagonals improperly.

The correct answer to choose will be based on these criteria regarding the number of triangles and the proper method of triangulation. If Figure 1 meets these criteria, select that; otherwise, select Figure 2 if it conforms to the rules but still shows 3 valid triangles.