When a regular polygon with n sides is decomposed into triangles using the same vertex, how many triangles are formed? (1 point)
When a regular polygon is decomposed, n - 2 triangles are formed, where r is the number of sides of the regular polygon. There are two fewer triangles than the number of the sides of the regular polygon.
When a regular polygon is decomposed, ni 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 more triangles than the number of the sides of the regular polygon.
When a regular polygon is decomposed, 2n 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 with n sides is decomposed into triangles using the same vertex, n - 2 triangles are formed.
When a regular polygon with n sides is decomposed into triangles using the same vertex, the correct answer is C) n + 2 triangles are formed. There are two more triangles than the number of sides of the regular polygon.
When a regular polygon with n sides is decomposed into triangles using the same vertex, the correct answer is: n - 2 triangles are formed.
To understand why, let's break it down step by step:
1. Start with a regular polygon with n sides. Each side of the polygon can be extended to create a triangle.
2. For each side of the polygon, a triangle is formed using that side as its base. Since there are n sides in total, n triangles can be formed.
3. However, when decomposing a polygon into triangles using the same vertex, the triangles will share two sides with the original polygon (assuming the vertex is not at one of the polygon's vertices). These shared sides are counted twice, once for each triangle they belong to.
4. Since every triangle has 3 sides, but 2 sides are shared between adjacent triangles, we need to subtract 2 from the total number of sides to account for this overlap.
5. Therefore, the total number of triangles formed is n - 2.
Please note that this formula only applies when using the same vertex for all the decomposed triangles. If different vertices are used, the number of triangles may vary.