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Journal for Geometry and Graphics 20 (2016), No. 1, 075--083 Copyright Heldermann Verlag 2016 Geometrical Shapes Allowing the Construction of the Midpoint of a Segment Using a Straightedge Only Victor Oxman Western Galilee College, P.O.Box 2125, Acre 24121, Israel victor.oxman@gmail.com Moshe Stupel Shaanan College, P.O.Box 906, Haifa 26109, Israel stupel@bezeqint.net Avi Sigler Technical College for Aviation Professions, Haifa, Israel anysig@walla.co.il Finding the middle point of a segment is one of the basic constructions for the case when there are restrictions requiring the use of an unmarked ruler (a straightedge) only. When a segment is given with its midpoint, this considerably expands the set of possible constructions using a straightedge only. It is well known that the middle point of a segment cannot be found by using a straightedge only; however, when certain geometrical shapes are given in the plane it is possible to carry out this construction. The paper gives 10 examples of shapes allowing elegant constructions of the midpoint of a certain segment using a straightedge only. Keywords: geometric constructions, constructions using a straightedge only, midpoint of a segment. MSC: 51M15 [ Fulltext-pdf (353 KB)] |