Use the image to answer the question.

Question

An illustration shows two square construction signs. Starting with the vertex on the left, the vertices are labeled A, B, C, and D. The sign on the left is labeled figure 1, and the sign on the right is labeled figure 2. In figure 1, lines connect the vertices A and C and B and D. In figure 2, a line connects the vertices B and D. An image on both signs shows a silhouette of a person holding a shovel.

Choose the correct decomposition of the polygon into n−2 triangles.

(1 point)
Responses

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 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.

Answer 1

The correct decomposition of the polygon (square) into \( n-2 \) triangles, where \( n \) is the number of vertices of the polygon, is as follows:

A square has 4 vertices (A, B, C, D), so \( n-2 = 4-2 = 2 \). Therefore, the polygon should be decomposed into 2 triangles.

• Figure 1 can be seen to decompose the square into 2 triangles by connecting both diagonals, resulting in 4 triangles total, but only 2 distinct triangles from the perspective of decomposing it down.
• Figure 2, however, directly connects the vertices B and D, indicating that it clearly provides a valid decomposition into 2 triangles.

Thus, the correct response is:

Figure 2 is the correct decomposition because it has n−2=4−2=2 triangles.