To determine how many triangles are formed when all diagonals are drawn from a vertex of a hexagon, let’s break it down step by step.
A hexagon has 6 vertices. If we take one vertex as a reference, we can only draw diagonals to the other non-adjacent vertices. Specifically, from one vertex of the hexagon, we can connect to the other vertices except for itself and its two adjacent vertices.
So, from one vertex, we can draw diagonals to 3 other vertices. These connections create triangles with the vertex we started from. For example, if we label the hexagon vertices as A, B, C, D, E, and F, and we draw diagonals from vertex A, we can connect to vertices C, D, and E. Each pair of these connections (C, D; C, E; D, E) will form a triangle with vertex A.
Thus, we can observe that the triangles formed are:
- Triangle ACD
- Triangle ACE
- Triangle ADE
In total, we form 3 triangles when all diagonals are drawn from one vertex in a hexagon.
To summarize, drawing all the diagonals from one vertex of a hexagon yields a total of 3 triangles.