A pentagon can be divided into how many triangles by drawing all of the diagonals from one vertex?

3 triangles contacting the diagonals from one vertex to the other vertices.

A triangle requires three lines. Starting from one vertex one side is made from one of the five existing lines. This line connect to the next vertex so that vertex cannot be used to create a diagonal. The second vertex and the third can be used to create diagonals making three triangles. The fourth vertex is connected by an existing line to the fifth or original vertex. This means it can not be used to form a diagonal or triangle.

five lines two lines are part of the vertex being used to draw the diagonals leaving only three lines. Three lines can be used to from three triangles.