Question

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.