DIVISION ACCORDING
TO A
GIVEN RATIO 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
Figure 48.Dividing a line into proportional parts.
Figure 49.Dividing a line into parts according to a given
ratio.
of doing this is shown in figure 49. 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.
ANGLES
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.
