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Figure 3.9

3.4 RELATIVE POSITION OF TWO LINES

There are three possible relative position of two straight lines:
- intersecting lines,
- parallel lines,
- skew lines.
The first two types of lines are coplanar lines.

Two intersecting lines
If two lines intersect, their projections will intersect, and the points of intersection of their
projections will be the projections of the point of their intersection.
Since the point of intersection is common to both lines, its frontal projection lies on the
frontal projection of each line, hence at their intersection; likewise the horizontal projection of the
point of intersection is the intersection of the horizontal projections. These two points, being the
projections of the same point, must lie on the same perpendicular to x.
Assume that both projections of one line AB (Fig. 3.10) and one projection, C 2D 2, of the other
line CD, intersect A 2B 2 at any point E 2. From E 2 drop a perpendicular to x until it intersects A 1B 1 at
E 1; through E 1 draw the horizontal projection of CD in any desired direction.

Figure 3.10

Two parallel lines
If two lines are parallel their projections are parallel.
To draw a line through a point and which is parallel to a given line.
If two lines are parallel in space, their projections on a plane are parallel. In general, if the
horizontal and frontal projections of two lines are parallel, the lines are parallel in space. Profile
lines are an exception and are parallel only when the profile projections of the line are parallel.
Let the given line and point be l and A, respectively (Fig 3.11). Draw the required line k
through point A, making k 1 parallel to l 1 and k 2 parallel to l 2.

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