C
C
B
D
B
D
A
Figure 1
E
A
E
Figure 2
Choose the correct decomposition of the regular polygon into n - 2 triangles.
(1 point)
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 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 5 triangles.
The correct answer is: Figure 1 is the correct decomposition because Figure 1 is decomposed into n - 2 = 5 - 2 = 3 triangles.
The correct decomposition of the regular polygon into n - 2 triangles is: Figure 1 is the correct decomposition because Figure 1 is decomposed into n - 2 = 5 - 2 = 3 triangles.
To determine the correct decomposition of the regular polygon into n - 2 triangles, we need to understand the concept of decomposing a polygon and the relationship between the number of sides of the polygon and the number of triangles formed.
A regular polygon is a polygon where all sides are equal in length and all angles are equal. The number of sides of a regular polygon is represented by 'n'. To decompose a regular polygon into triangles, we need to divide it into smaller parts that form triangles.
The formula to calculate the number of triangles formed when decomposing a regular polygon is given by n - 2, where 'n' is the number of sides of the polygon.
Looking at the given options:
- Option 1: Figure 1 is the correct decomposition because Figure 1 is decomposed into n - 2 = 5 - 2 = 3 triangles. This aligns with the formula n - 2.
- Option 2: Figure 1 is the correct decomposition because Figure 1 is decomposed into triangles that are equal sizes. The size or dimensions of the triangles are not a determining factor for the correct decomposition. The number of triangles formed is what matters.
- Option 3: Figure 2 is the correct decomposition because Figure 2 is decomposed into n - 2 triangles. However, it does not specify the value of 'n', so we cannot determine the number of triangles formed using this information alone.
- Option 4: Figure 2 is the correct decomposition because Figure 2 is decomposed into 5 triangles. This option is incorrect because it does not follow the formula n - 2.
Therefore, the correct answer is Option 1: Figure 1 is the correct decomposition because Figure 1 is decomposed into n - 2 = 5 - 2 = 3 triangles.