An illustration shows a decagon. Starting with the top left vertex, the vertices are labeled A, B, C, D, E, F, G, H, I, and J moving clockwise around the polygon.
Decompose the decagon into n−2
triangles.
(1 point)
Responses
An illustration shows a decagon. Starting with the top left vertex, the vertices are labeled A, B, C, D, E, F, G, H, I, and J moving clockwise around the polygon. Lines inside the decagon connect the vertices A and F, B and G, C and H, D and I, and E and J. All the lines intersect at a point in the middle of the decagon.
Image with alt text: An illustration shows a decagon. Starting with the top left vertex, the vertices are labeled A, B, C, D, E, F, G, H, I, and J moving clockwise around the polygon. Lines inside the decagon connect the vertices A and F, B and G, C and H, D and I, and E and J. All the lines intersect at a point in the middle of the decagon.
An illustration shows a decagon. Starting with the top left vertex, the vertices are labeled A, B, C, D, E, F, G, H, I, and J moving clockwise around the polygon. Lines inside the decagon connect the vertices A and C, A and D, A and E, A and F, A and G, A and H, and A and I.
Image with alt text: An illustration shows a decagon. Starting with the top left vertex, the vertices are labeled A, B, C, D, E, F, G, H, I, and J moving clockwise around the polygon. Lines inside the decagon connect the vertices A and C, A and D, A and E, A and F, A and G, A and H, and A and I.
An illustration shows an decagon. Starting with the top left vertex, the vertices are labeled A, B, C, D, E, F, G, H, I, and J moving clockwise around the polygon. Lines inside the decagon connect the vertices A and F, B and G, and D and I. All the lines intersect at a point in the middle of the decagon.
Image with alt text: An illustration shows an decagon. Starting with the top left vertex, the vertices are labeled A, B, C, D, E, F, G, H, I, and J moving clockwise around the polygon. Lines inside the decagon connect the vertices A and F, B and G, and D and I. All the lines intersect at a point in the middle of the decagon.
An illustration shows a decagon. Starting with the top left vertex, the vertices are labeled A, B, C, D, E, F, G, H, I, and J moving clockwise around the polygon. Lines inside the decagon connect the vertices A and F, B and E, C and I, D and H, and G and J.
Image with alt text: An illustration shows a decagon. Starting with the top left vertex, the vertices are labeled A, B, C, D, E, F, G, H, I, and J moving clockwise around the polygon. Lines inside the decagon connect the vertices A and F, B and E, C and I, D and H, and G and J.
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To decompose a decagon into triangles, we can apply the concept of polygon triangulation. A decagon has 10 sides and can be divided into \( n - 2 \) triangles where \( n \) is the number of sides. In this case, \( n = 10 \), so we can create \( 10 - 2 = 8 \) triangles.
Among the options you provided, the second illustration shows lines that connect multiple vertices to one vertex (vertex A). This method typically decomposes the decagon correctly because it results in the creation of triangles by making several connections from a single vertex to other non-adjacent vertices.
Therefore, the response that best represents the decomposition of a decagon into triangles is the second image, which connects the vertices A and C, A and D, A and E, A and F, A and G, A and H, and A and I, achieving the required triangulation.
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