Geometry for Elementary School/Copying a line segment

Constructing equilateral triangle Copying a line segment Copying a triangle This construction copies a line segment to a target point T. The construction is based on Book I, prop 2. The construction Let A be one of the end points of . Note that we are just giving it a name here. (We could replace A with the other end point B)225px Draw a line segment 225px Construct an equilateral triangle (a triangle that has as one of its sides).225px Draw the circle , whose center is A and radius is .225px Draw a line segment starting from D going through A until it intersects and let the intersection point be E . Get segments and .225px Draw the circle , whose center is D and radius is .225px Draw a line segment starting from D going through T until it intersects and let the intersection point be F. Get segments and .225px Claim The segment is equal to and starts at T.225px Proof Segments and are both from the center of to its circumference. Therefore they equal to the circle radius and to each other.225px Segments and are both from the center of to its circumference. Therefore they equal to the circle radius and to each other.225px equals to the sum of its parts and .225px equals to the sum of its parts and .225px The segment is equal to since they are the sides of the equilateral triangle .225px Since the sum of segments is equal and two of the summands are equal so are the two other summands and .225px Therefore equals .225px it:Geometria per scuola elementare/Copia di un segmento