Choose the correct decomposition of the polygon into n−2 triangles. (1 point) Responses 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 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 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. Figure 1 is the correct decomposition because it has 4 triangles of the equal size.

Answer 1

To determine the correct decomposition of a polygon into \( n - 2 \) triangles, we first need to know the number of sides \( n \) of the polygon. The formula \( n - 2 \) gives the number of triangles resulting from triangulating a polygon.

1. If the polygon has 4 sides (a quadrilateral), then:
   • \( n = 4 \)
   • The number of triangles formed by decomposing the polygon would be \( 4 - 2 = 2 \).

From the responses provided:

• "Figure 2 is the correct decomposition because it has \( n - 2 = 4 - 2 = 2 \) triangles." This is correct for a quadrilateral.
• "Figure 1 is the correct decomposition because Figure 1 is decomposed into 4 triangles that are not equal sizes." This suggests that Figure 1 might be for a polygon with more than 4 sides.
• "Figure 1 is the correct decomposition because it has 4 triangles of equal size." This also suggests an incorrect count for a quadrilateral.

Therefore, if we assume we are dealing with a quadrilateral, the correct response would be:

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

If the polygon has more than 4 sides, different figures might be correct, but based on the information given, this is the most accurate selection.