Geometry for Elementary School/Bisecting a segment

Bisecting an angle Congruence and similarity In this chapter, we will learn how to bisect a segment. Given a segment , we will divide it to two equal segments and . The construction is based on book I, proposition 10. The construction Construct the equilateral triangle on . Bisect an angle on using the segment . Let C be the intersection point of and . Claim Both and are equal to half of . The proof and are sides of the equilateral triangle . Hence, equals . The segment equals to itself. Due to the construction and are equal. The segments and lie on each other. Hence, equals to and equals to . Due to the Side-Angle-Side congruence theorem the triangles and congruent. Hence, and are equal. Since is the sum of and , each of them equals to its half. it:Geometria per scuola elementare/Bisezione di un segmento