Understanding Engineering Mathematics

In Figure 5.11 AOCand COBare supplementary. An angle of 90°is a rotation
through a quarter circle and is called aright angle. In diagrams a right angle between
two lines is always denoted by a small square at their intersection – if this is not present
then you cannotassumethe angle is 90°, even though it may look like it on the diagram.
Angles which add up to 90°are calledcomplementary angles. Two lines which intersect
at right angles are said to beperpendicularto each other. Angles between 0°and 90°are
calledacute. Angles between 90°and 180°are calledobtuse. Angles greater than 180°
are calledreflex.
When two lines intersect,vertically opposite anglesare equal:

bb

a

a

Figure 5.12Intersecting lines.

Two lines areparallelif they do not intersect, no matter how far they are extended – we
say they ‘meet at infinity (wherever that is)’. We denote parallel lines by equal numbers
of arrow-heads as in Figure 5.13. Equal angles are denoted by equal numbers of crossbars
on the angle arcs.

a

b

c

Figure 5.13Angles on parallel lines.

As noted earlier, remember that we are talking aboutplane geometryhere. Parallel
lines drawn on the surface of a sphere for example do not satisfy the sorts of properties
we will be discussing for parallel lines in a plane.
The line drawn crossing the parallel lines in Figure 5.13 is called atransversal.In
Figure 5.13 pairs of angles such asaandb, on opposite sides of the transversal are called
alternate angles, while pairs of anglesaandcare calledcorresponding angles.Fortwo
parallel lines, as shown in Figure 5.13 alternate angles are equal, as are corresponding
angles, i.e.a=b=c.