Geometry for Elementary School/Bisecting an angle

Why are the constructions not correct? Bisecting a segment BISECT ANGLE Use a compass to find points D and E, equidistant from the vertex, point B. Draw the line .396 px Construct an equilateral triangle on with third vertex F and get . (Lines DF and EF are equal in length).396 px Draw the line .396 px Claim The angles , equal to half of . The proof is a segment from the center to the circumference of and therefore equals its radius. Hence, equals . and are sides of the equilateral triangle . Hence, equals . The segment equals to itself Due to the Side-Side-Side congruence theorem the triangles and congruent. Hence, the angles , equal to half of . Note We showed a simple method to divide an angle to two. A natural question that rises is how to divide an angle into other numbers. Since Euclid's days, mathematicians looked for a method for trisecting an angle, dividing it into 3. Only after years of trials it was proven that no such method exists since such a construction is impossible, using only ruler and compass. Exercise Find a construction for dividing an angle to 4. Find a construction for dividing an angle to 8. For which other number you can find such constructions? it:Geometria per scuola elementare/Bisettrice di un angolo