Use the image to answer the 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 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.
Figure 1 is the correct decomposition because it has 4 triangles of the equal size.
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 2 triangles that are equal sizes.
Figure 1 is the correct decomposition because Figure 1 is decomposed into 2 triangles that are equal sizes.
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The correct decomposition of the polygon is as follows:
Figure 1 is the correct decomposition because it is decomposed into 2 triangles that are equal sizes.
which option?
I apologize for the confusion. It seems that the correct option was not specified in the original response.
Based on the given information, the correct option would be:
Figure 1 is the correct decomposition because it is decomposed into 4 triangles that are not equal sizes.
To answer the question, we need to analyze the given illustration. The illustration consists of two square construction signs labeled figure 1 and figure 2.
In figure 1, the vertices A, B, C, and D are connected by lines. This results in the polygon being decomposed into four triangles. These triangles are not of equal size. Therefore, figure 1 cannot be the correct decomposition.
In figure 2, only the vertices B and D are connected by a line. This means that the polygon is decomposed into two triangles. According to the formula for decomposition of a polygon, n-2 triangles are needed, where n is the number of vertices in the polygon. In this case, since the polygon has 4 vertices, the number of triangles needed is 4-2=2. Thus, figure 2 is the correct decomposition as it fulfills this requirement.
Therefore, the correct answer is:
Figure 2 is the correct decomposition because it has n-2 = 4-2 = 2 triangles.