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 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 5 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 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 triangles that are equal sizes.

Answer 1

To determine the correct decomposition of a regular polygon into \( n - 2 \) triangles, we first need to consider the number of sides \( n \) of the polygon.

For a regular polygon with \( n \) sides:
- The formula for decomposing it into triangles is \( n - 2 \).
- This means that for a polygon with 5 sides (a pentagon), the decomposition should result in \( 5 - 2 = 3 \) triangles.

**Evaluating the Options:**
- If Figure 1 is decomposed into 3 triangles, and it represents a pentagon (5 sides), then it correctly follows the formula of \( n - 2 \).
- If Figure 2 is decomposed into 5 triangles, that does not follow \( n - 2 \), as \( 5 - 2 = 3 \).

Thus, the correct response about the decomposition of a pentagon into triangles should be:
**Figure 1 is the correct decomposition because Figure 1 is decomposed into \( n - 2 = 5 - 2 = 3 \) triangles.**

This option accurately reflects the mathematical principle behind decomposing a polygon into triangles based on its number of sides.