Straightedge and compass constructions

geometric problem

way of drawing geometric objects using only an idealized compass and straightedge

geometric problem of constructing a cube with twice the volume of a given cube

construction of an angle equal to one third a given angle

thumb|upright=1.2|Girih pattern with inlaid floral decoration from :en:Shah-i-Zinda|Shah-i-Zinda in [[Samarkand, Uzbekistan]]

theorem in geometry

theorem

thumb|The perpendicular bisectors of the three sides of a triangle pass through the triangle's circumcenter.