Triangle Decomposition of Polygons Practice

Question

Complete this assessment to review what you've learned. It will not count toward your grade.
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Question
Use the image to answer the question.

An illustration shows two dodecagons. The dodecagon on the left is labeled figure 1, and the dodecagon on the right is labeled figure 2. Starting at the bottom left vertex of both figures, the vertices are labeled A, B, C, D, E, F, G, H, I, J, K, and L. In both figures, lines connect the vertices F and H, F and I, F and J, F and K, F and L, F and A, F and B, and F and C.

Select the correct decomposition of the dodecagon into n−2
triangles.

(1 point)
The correct decomposition is Figure
.
Remaining Attempts : 3

Answer 1

In order to decompose a dodecagon (which has 12 sides) into triangles, you need to connect non-adjacent vertices (diagonals) in such a way that the polygon is subdivided into triangles without overlapping.

Each time you connect a diagonal, you essentially reduce the polygon's number of triangles by one. For an n-sided polygon, the number of triangles that can be formed in the decomposition is given by \( n - 2 \). For a dodecagon \( n = 12 \), therefore, the decomposition would yield \( 12 - 2 = 10 \) triangles.

Given that both figure 1 and figure 2 use the same vertex F and connect to various vertices, you’ll need to identify which figure uses appropriate diagonals that do not overlap and successfully divides the dodecagon into 10 triangles.

If you're unable to access or visualize the figures, it would be helpful to look for a decomposition that uses vertex F in a consistent and effective manner creating triangles.

Please check the figures provided and select the one that meets this requirement to complete your answer. If there's a specific detail you're uncertain about, feel free to provide more information or ask follow-up questions!