You may be required to divide a line into parts so that the ratio between the whole line and one of the parts is the same as that between two other lines. A method

of doing this is shown in figure 4-9. Here, it is required that AB be divided so that the ratio between AB and a part of AB is the same as the ratio between CD and EF. From A, draw a ray line AG at a convenient acute angle from AB. On AG, lay off AH equal to EF and AI equal to CD. Draw a line from I to B, and use a straightedge and triangle to project H to J on a line parallel to IB. The ratio of AB to AJ is the same as that of CD to EF.

You already know how to lay off an angle of given size with a protractor, or trigonometrically by the use of the tangent or the chord method.