What is the difference between unique triangle, more than one triangle, and no triangle?
To understand the differences between unique triangle, more than one triangle, and no triangle, we need to understand what constitutes a triangle.
A triangle is a polygon with three sides. It is formed by connecting three non-collinear points, i.e., three points that do not lie on the same straight line. Now, let's break down each scenario:
1. Unique Triangle: In this case, we have exactly one triangle. This means that there are three non-collinear points which can be connected to form a single closed polygon with three sides. All the sides and angles of this triangle are well-defined.
2. More than One Triangle: Here, we have multiple triangles. To have more than one triangle, we need at least four non-collinear points. By connecting these points in different combinations, we can form multiple triangles with different side lengths and angles. The exact number of triangles will depend on the total number of non-collinear points provided.
3. No Triangle: In this situation, we don't have a triangle at all. This occurs when the given points are collinear, meaning they lie on the same straight line. If the points do not form a closed polygon with three sides, then they cannot create a triangle.
Remember, in order to determine if the given points form a triangle or not, you can use the triangle inequality theorem. It states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. If this condition is not satisfied for any combination of the given points, then we do not have a triangle.