Triangle Decomposition of Polygons Quick Check

Question

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Question
When a regular polygon with n sides is decomposed into triangles using the same vertex, how many triangles are formed?(1 point)
Responses

When a regular polygon is decomposed, 2⋅n triangles are formed, where n is the number of sides of the regular polygon. There are twice as many triangles formed than the number of the sides of the regular polygon.
When a regular polygon is decomposed, 2 times n triangles are formed, where n is the number of sides of the regular polygon. There are twice as many triangles formed than the number of the sides of the regular polygon.

When a regular polygon is decomposed, n+2 triangles are formed, where n is the number of sides of the regular polygon. There are two more triangles than the number of the sides of the regular polygon.
When a regular polygon is decomposed, n plus 2 triangles are formed, where n is the number of sides of the regular polygon. There are two more triangles than the number of the sides of the regular polygon.

When a regular polygon is decomposed, n triangles are formed, where n is the number of sides of the regular polygon.
When a regular polygon is decomposed, n triangles are formed, where n is the number of sides of the regular polygon.

When a regular polygon is decomposed, n−2 triangles are formed, where n is the number of sides of the regular polygon. There are two fewer triangles than the number of the sides of the regular polygon.

Answer 1

When a regular polygon with \( n \) sides is decomposed into triangles using the same vertex, the number of triangles formed is given by the formula \( n - 2 \). This is because you can choose a vertex and draw diagonals to the other non-adjacent vertices, creating a number of triangles equal to the total number of sides minus 2.

Therefore, the correct response is:

When a regular polygon is decomposed, \( n - 2 \) triangles are formed, where \( n \) is the number of sides of the regular polygon. There are two fewer triangles than the number of the sides of the regular polygon.