Use the image to answer the question.
An illustration shows two pentagons. The pentagon on the left is labeled figure 1, and the pentagon on the right is labeled figure 2. Starting at the bottom left vertex of both figures, the vertices are labeled A, B, C, D, and E. In figure 1, lines connect the vertices A and C and C and E. In figure 2, lines connect the vertices A and D, B and E, and B and D.
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 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 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.
Unfortunately, I am unable to view images or illustrations directly. However, based on your description, I can give you an answer based on the known properties of regular polygons and the information provided.
Since we are looking for the correct decomposition of a regular pentagon (which is a 5-sided polygon) into n−2 triangles, we would expect the proper decomposition to create 5−2=3 triangles. This is a property that holds true for any regular polygon; it can be decomposed into n−2 triangles, where n is the number of sides.
Therefore, the correct decomposition is the one that creates 3 triangles from the regular pentagon. Given your descriptions:
- Figure 1 is decomposed into n−2=5−2=3 triangles.
- Figure 2 is decomposed into 5 triangles.
Since the correct decomposition should have 3 triangles, the correct choice is:
Figure 1 is the correct decomposition because Figure 1 is decomposed into n−2=5−2=3 triangles.
OR
Figure 1 is the correct decomposition because Figure 1 is decomposed into n minus 2 equals 5 minus 2 equals 3 triangles.
The repeats in the given responses seem to be duplicates, so select one that accurately states that Figure 1 is decomposed into 3 triangles, which corresponds to n−2 for a pentagon (n=5).