Question 145
a. A convex heptagon is divided into triangles by drawing its diagonals. Prove that in such case you can obtain 5 or 7 triangles, but can not get 6 triangles.
b. Prove that there exists nonconvex heptagon that can be divided by internal diagonals into 6 triangles. Internal diagonal of a polygon $M$ is a segment connecting the two non-neighbouring vertices of $M$ and does not go beyond the figure.
b. Prove that there exists nonconvex heptagon that can be divided by internal diagonals into 6 triangles. Internal diagonal of a polygon $M$ is a segment connecting the two non-neighbouring vertices of $M$ and does not go beyond the figure.