Elements IV.11
- Author:
- Gianluca Occhetta
Construction of the regular pentagon
The triangle ABC is the one constructed in Proposition IV.10.
The sides of the pentagon are congruent since, by constructions, the angles HDG, DHI, IHG, JGH and JGD are congruent. Then we joint the vertices with the center of the circle. The triangles DOI, IOG, GOH, HOJ, JOD are (isosceles) and congruent by I.8, hence the angles of the pentagon are congruent being sums of congruent angles.