How many triangles are formed when all diagonals are drawn from a vertex of a hexagon?

When you draw all the diagonals from a single vertex of a hexagon, you can create several triangles. Let’s break it down step by step.

A hexagon has six sides, and when you select any vertex to start drawing diagonals, you will connect that vertex to non-adjacent vertices. Each vertex connects to the other vertices across the sides of the hexagon, and diagonals can be drawn to three of the other vertices (since two vertices are adjacent to the chosen vertex).

For example, let’s label the vertices of the hexagon as A, B, C, D, E, and F in a clockwise direction. If we choose vertex A:

  1. Drawing a diagonal to vertex C forms triangle ABC.
  2. Drawing a diagonal to vertex D forms triangle ABD.
  3. Drawing a diagonal to vertex E forms triangle ABE.

By drawing these three diagonals, we have created three distinct triangles: ABC, ABD, and ABE. Importantly, note that these triangles share the same vertex A but are enclosed by different combinations of the other vertices.

To summarize, when you draw all the diagonals from a single vertex of a hexagon, you will form a total of three triangles.

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