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10b. Parallel Lines
• Parallel lines do not have any common point between them
• Parallel lines are seen as parallel in adjacent views, exception
to this when the lines are perpendicular to the FL, the lines
may or may not be parallel
10b. Parallel Lines
• To find out if the lines are parallel, even if the lines are
perpendicular to the FL, it is best to draw the 3rd view
• If it is required to get the lines parallel, then use one view,
draw the lines parallel and complete the 3rd view
10b. Parallel Lines
bF
aFkF
jF
F P
kPaP
bH
kHaH
H
F
jH
jP
bP
H
F
F P
aH
aF
aP
bH
bF
bP
jH
jF
jP
kH
kF kP
10c. Intersecting Lines
• Intersecting lines
have one common
point between them
• The projection of the
points must be
aligned in adjacent
views
• If they are, then the
lines are intersecting
• If not, they are
skewed
H
F
F P
aH
aF
aP
bH
bF
bPeF
gF
gH
eH
eP
gP
H
F
F P
aH
aF
aP
bH
bF
bP
jH
jF
jP
kH
kF kP
eFbF
aF
gF gP
F PeP
aP
bH
aH
H
F
gH
eH
bP
10c. Intersecting Lines
• Intersecting lines
have one common
point between them
• The projection of the
points must be
aligned in adjacent
views
• If they are, then the
lines are intersecting
• If not, they are
skewed
eFbF
aF
gF gP
F PeP
aP
bH
aH
H
F
gH
eH
bP
10c. Intersecting Lines
• Intersecting lines
have one common
point between them
• The projection of the
points must be
aligned in adjacent
views
• If they are, then the
lines are intersecting
• If not, they are
skewed
bF
aF
F P
aP
bH
aH
H
F
bP
10c. Coincident lines
bF
aF
F P
aP
bH
aH
H
F
bP
cH
dH
cF
dF
cP
dP
10c. Coincident lines
H
F
aH
aF
bH
bF
sH
sF
11. Location of a line
Locate a line // to a given line passing through a point
H
F
aH
aF
bH
bF
jH
jF
kH
kF
sH
sF
11. Location of a line
Locate a line // to a given line passing through a point
12. True distance between 2 // lines
Two auxiliary views
H
F
aH
aF
bH
bF
jH
jF
kH
kF
HA
A A1
aA
kA bA
jA
kA1=jA1
aA1=bA1
Two auxiliary views
H
F
aH
aF
bH
bF
jH
jF
kH
kF
HA
A A1
aA
kA bA
jA
kA1=jA1
aA1=bA1
12. True distance between 2 // lines
x
x
Y
Y
Y’
Y’
X’
X’
H
F
aH
aF
bH
bF
jH
jF
kH
kF
HA
A A1
aA
kA bA
jA
kA1=jA1
aA1=bA1
Distance between the
two points gives the
true distance between
parallel lines
12. True distance between 2 // lines
13. Perpendicular lines
H
F
aH
aF
bH
bF
cH
cF
90° • A 90° angle appears in
true size in any view
showing one leg in TL
provided the other leg
does not appear as point
view
• Two intersecting lines are
perpendicular if the TL
projection is making 90°
with the other line
13. Perpendicular lines
Mechanical Engineering Drawing
MECH 211
LECTURE 5
The objectives of the lecture
• Continue to acquire knowledge in the Descriptive
Geometry – point and line concepts
• Distance form a point to a line
• Location of a perpendicular line at a give location on a
line
• Non-intersecting lines – skew lines
• Shortest distance between skew lines
• Location of a line through a given point and intersecting
two skew lines
• Continue to acquire knowledge in the Descriptive Geometry – point and line and plane concepts
• Representation of a plane surface
• Relative position of a line versus a plane
• Location of a line on a plane
• Location of a point on a plane
• True-length lines in a plane
• Strike of a plane – bearing of the horizontal line in a plane
• Edge view of a plane – planes that appear as edge view in the principal views
• Slope of a plane – the angle the plane is doing with the horizontal plane from T.E.V.)
The objectives of the lecture - Contd
Distance form a point to a line
Distance form a point to a line
Distance form a point to a line
Distance form a point to a line
Distance form a point to a line
Distance form a point to a line
Location of a perpendicular line at a give location on a line
Location of a perpendicular line at a give location on a line
Location of a perpendicular line at a give location on a line
Location of a perpendicular line at a give location on a line
Location of a perpendicular line at a give location on a line
Location of a perpendicular line at a give location on a line
Non-intersecting lines – skew lines
Non-intersecting lines – skew lines
Non-intersecting lines – skew lines
Non-intersecting lines – skew lines
Non-intersecting lines – skew lines
Shortest distance between skew lines
Shortest distance between skew lines
Shortest distance between skew lines
Shortest distance between skew lines
Shortest distance between skew lines
Shortest distance between skew lines
Shortest distance between skew lines
through a given point and intersecting two skew lines
Location of a line
through a given point and intersecting two skew lines
Location of a line
through a given point and intersecting two skew lines
Location of a line
through a given point and intersecting two skew lines
Location of a line
through a given point and intersecting two skew lines
Location of a line
through a given point and intersecting two skew lines
Location of a line
mF
bF
aF
nF
mH
aH
nH
bH
A plane is defined by one of
the below:
1) Two parallel lines
2) Two intersecting lines
3) One line and a point
external to the line
4) Three point that are not
positioned along the same line
cF
cH
Representation of a plane surface
bF
aF
aH
bH
A line is located in a plane if
all the points of that line are
in that plane. However, is
sufficient to show that two
points that belong to the line
belong to the plane too.
cF
cH
Relative position of line Vs. plane
mF
bF
aF
nF
mH
aH
nH
bH
A line is located in a plane if
all the points of that line are
in that plane. However, is
sufficient to show that two
points that belong to the line
belong to the plane too.
cF
cH
Line MN is located in the
plane ABC since M is
simultaneously located in AB
and MN and N on AC and MN.
Relative position of line Vs. plane
Relative position of line Vs. plane
mF
bF
aF
nF
mH
aH
nH
bH
A line is located in a plane if
all the points of that line are
in that plane. However, is
sufficient to show that two
points that belong to the line
belong to the plane too.
cF
cH
dH
eH
dF
eF
jH
jF
Line DE is parallel to the
plane ABC since is
parallel to a line (MN)
that is contained in that
plane
Line MN is located in the
plane ABC since M is
simultaneously located in AB
and MN and N on AC and MN.
Relative position of line Vs. plane
mF
bF
aF
nF
mH
aH
nH
bH
A line is located in a plane if
all the points of that line are
in that plane. However, is
sufficient to show that two
points that belong to the line
belong to the plane too.
cF
cH
pH
qH
iH
iF
pF
qF
dH
eH
dF
eF
jH
jF
Line DE is parallel to the
plane ABC since is
parallel to a line (MN)
that is contained in that
plane
Line PQ is intersecting
the plane ABC in the
point I.
Line MN is located in the
plane ABC since M is
simultaneously located in AB
and MN and N on AC and MN.
mF
bF
aF
nF
mH
aH
nH
bH
A line is located in a plane if
all the points of that line are
in that plane. However, is
sufficient to show that two
points that belong to the line
belong to the plane too.
cF
cH
pH
qH
iH
iF
pF
qF
dH
eH
dF
eF
jH
jF
Line DE is parallel to the
plane ABC since is
parallel to a line (MN)
that is contained in that
plane
Line PQ is intersecting
the plane ABC in the
point I.
Apart from the three
positions, there is no
other relative position on
a line with a plane.Line MN is located in the
plane ABC since M is
simultaneously located in AB
and MN and N on AC and MN.
Relative position of line Vs. plane
mF
bF
aF
nF
mH
aH
nH
bH
A line is located in a plane if
all the points of that line are
in that plane. However, is
sufficient to show that two
points that belong to the line
belong to the plane too.
Line MN is located in the
plane ABC since M is
simultaneously located in AB
and MN and N on AC and MN.
cF
cH
Location of a line on a plane
Location of a line on a plane
Can you locate the line 4-5 in the plane 1-2-3
bF
aF
nF
aH
nH
bH
cF
cHiH
iF
Location of a point on a plane
mF
bF
aF
nF
mH
aH
nH
bH
cF
cHiH
iF
A point I is located
on a plane if is
located on a line that
belongs to that plane.
Location of a point on a plane
Location of a point on a plane
Using Parallelism
Can you locate the point 4 in the plane 1-2-3
Location of a point on a plane
Locate a point which is 10mm above point 2 and 12mm behind
point 3
bF
aF
aH
bH
cF
cHmH
mF
nH
nF
iH
iF
jH
jFLine IJ is a front line.
iFjF is the true length of the
line IJ.
Line MN is a horizontal
line. mHnH is the true
length of the line MN.
True Length line lies on the plane
mF
bF
aF
nF
mH
aH
nH
bH
cF
cH
Line MN is a horizontal
line. mHnH is the true
length of the line MN.
The bearing of this line
represents the strike of
the plane.
N
N59°E
Strike of a plane
bF
aF
aH
bH
cF
cH
Edge View of a plane
Edge View of a plane
bF
aF
aH
bH
cF
cH
bF
aF
aH
bH
cF
cH Elevation
View
E.V
.
Horizontal plane
The Edge View (EV) of the plane is built in
an auxiliary view adjacent with the
Horizontal (Top) view. The angle of the EV
of the plane with the horizontal direction
represents the slope (dip ) of the planenFmF
mH
nH
Slope (dip) of a plane
Shortest line from a point to plane
bF
aF
aH
bH
cF
cH
To find the shortest line from point
to plane
Shortest line from a point to plane
TL cA
bA
aA
mF
bF
aF
nF
mH
aH
nH
bH
cF
cH
Find the EV of
plane
Shortest line from a point to plane
TL
eF
eH
eA
cA
bA
aA
mF
bF
aF
nF
mH
aH
nH
bH
cF
cH
Find the EV of
plane
Project point in
that view
Shortest line from a point to plane
TL
eF
eH
eA
cA
bA
aA
eA
eH
eF
mF
bF
aF
nF
mH
aH
nH
bH
cF
cH
Find the EV of plane
Project point in that
view
Draw perp from
point to EV
Traceback with perp
from TL in the HV
For FV use distance
mF
bF
aF
nF
mH
aH
nH
bH
cF
cHTL
eF
eH
eA
cA
bA
aA
eA
eH
eF
Horizontal directionrA
rH
rF
Shortest grade line - point to plane
Shortest grade line - point to plane
cH
cF
bH
aH
aF
bF
Shortest grade line - point to plane
aA
bA
cATL
cH
cF
bH
nH
aH
mH
nF
aF
bF
mF
Shortest grade line - point to plane
bA
aA
cA
eA
eH
eF
TL
cH
cF
bH
nH
aH
mH
nF
aF
bF
mF
Shortest grade line - point to plane
eF
eH
eA
aA
bA
cA
eA
eH
eF
TL
cH
cF
bH
nH
aH
mH
nF
aF
bF
mF
Shortest grade line - point to plane
rF
rH
rAHorizontal direction
eF
eH
eA
aA
bA
cA
eA
eH
eF
TL
cH
cF
bH
nH
aH
mH
nF
aF
bF
mF
qF
qH
Line at 20° slopeqA
rF
rH
rA
The slope could be
shown ONLY IN AN ELEVATION VIEW
Horizontal direction
eF
eH
eA
aA
bA
cA
eA
eH
eF
TL
cH
cF
bH
nH
aH
mH
nF
aF
bF
mF
Shortest grade line - point to plane
