Projection of planes

1. Inclined to one R.P and perpendicular to other R.P.

2. Projections of planes inclined to one R.P and perpendicular
to other R.P.
When a plane is inclined to a reference plane, its
projections may be obtained in two stages.
In the initial stage, the plane is assumed to be parallel to
that reference plane to which it has to be made inclined
In the second stage, it is tilted to the required inclination.

3. In both the cases, if :
1. An edge or side is in a plane then that edge
should be made perpendicular to reference line
in the first stage
2. A corner is in plane then the line joining that
corner and center of the plane should be made
parallel to reference line in the first stage

4. Projections of Planes inclined to
both the planes
When a plane has its surface inclined to one
plane and an edge or a diameter or a diagonal
parallel to that plane and inclined to the other
plane, its projections are drawn in three stages

5. Read problem and answer following questions
1.Surface inclined to which plane?
Horizontal Plane - 45°
2.Whether Corner or Edge is on HP?
Edge
3. Assumption for initial position?
Entire surface parallel to HP and an edge ^ to VP
4. So which view will show True shape?
Top View
5. So pentagon should be drawn above or below the Reference Line?
Draw pentagon below X-Y line, taking one side vertical.
Problem 1:
A regular pentagon of 30 mm sides is
resting on HP on one of it’s sides with it’s
surface 450 inclined to HP. Draw it’s
projections when the side in HP makes 300
angle with VP
(a’)
b’ d’
b1
d
c1
a
c’(e’)
b
c
d1
b’1
a1
e’1
c’1
d’1
a1
b1
c1
d1
d
’
(
a
’
)
b
’
c’(e’)
e1
e1
a’1
X Y
450
300
e
SURFACE AND SIDE INCLINATIONS
ARE DIRECTLY GIVEN.

7. Problem 2: A square ABCD of 50 mm side has its corner A in the H.P., its diagonal AC inclined at 30º
to the H.P. and the diagonal BD inclined at 45º to the V.P. and parallel to the H.P. Draw its projections.
X Y
a
b
c
d
45º
50
a’ d’(b’) c’ a’
d’ (b’)
c’
30º
a1
c1
b1
d1
45º
a1
c1
b1
d1
b1’
c1’
d1’
Corner A is in HP
What we can interpret?
The line joining A and centre of
the plane should be made parallel
to reference line in the first stage
Incline AC at 30º to the H.P.
i.e. incline the First Front
View (FFV) at 30º to the HP
Incline BD at 45º to the V.P.
a1’

9. 3. A hexagonal plane of side 30 mm has an edge
on the H.P. Its surface is inclined at 45° to the H.P.
and the edge on which the plane rests is inclined
at 30° to the V.P. Draw its projections.

11. Problem 4:
A 300 – 600 set square of longest side
100 mm long, is in VP and 300 inclined
to HP while it’s surface is 450 inclined
to VP. Draw it’s projections
(Surface & Side inclinations directly given)
Read problem and answer following questions
1 .Surface inclined to which plane? ------- VP
2. Assumption for initial position? ------// to VP
3. So which view will show True shape? --- FV
4. Which side will be vertical? ------longest side.
c1
X Y
300
450
a’1
b’1
c’1
a
c
a’
a
b1
b’
b
a1
b
c
a’1
b’1
c’1
c’
Hence begin with FV, draw triangle above X-Y
keeping longest side vertical.
Surface // to Vp Surface inclined to Vp
side inclined to Hp

13. Draw the projections of a circle of 50mm diameter resting
in the HP on a point A on the circumference, its plane
inclined at 45 degree to the HP and
(a) The top view of the diameter AB making 30 degree
angle with the VP.
(b) The diameter AB making 30 degree angle with the VP

15. Q4: A Hexagonal plane of 30mm has an
edge in the VP. The surface of the
plane is inclined at 45° to the VP and
the edge on which it rests is inclined at
30° to the HP. Draw its projections.
Read problem and answer following questions
1.Surface inclined to which plane?
Vertical Plane - 45°
2.Whether Corner or Edge is on HP?
Edge
3. Assumption for initial position?
Entire surface parallel to VP and an edge ^ to HP
4. So which view will show True shape?
Front View
5. So pentagon should be drawn above or below the Reference Line?
Draw hexagon above X-Y line, taking one side vertical.

16. Problem 5:
Draw the projections of a circle of 50mm diameter resting in the HP on a point A on the
circumference, its plane inclined at 45° to the HP and
(a) The top view of the diameter AB making 30° angle with the VP.
(b) The diameter AB making 30° angle with the VP.

17. Example
A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of the
pentagon is parallel to the H.P. and 30 mm above it and also inclined at 60o to the V.P. Draw
its projections.

18. Example 4:
A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of the
pentagon is parallel to the H.P. and 30 mm above it and also inclined at 60o to the V.P. Draw
its projections.
y
x
a'
d'
e'
c'
b'
a
b
c
d
e
30

19. Example 4:
A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of the
pentagon is parallel to the H.P. and 30 mm above it and also inclined at 60o to the V.P. Draw
its projections.
y
x
a'
d'
e'
c'
b'
a
b
c
d
e
30
b'
a'
d'
e'
c'
4
5
°
a
b
c
e
d

20. Example 4:
A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of the
pentagon is parallel to the H.P. and 30 mm above it and also inclined at 60o to the V.P. Draw
its projections.
y
x
a'
d'
e'
c'
b'
a
b
c
d
e
30
b'
a'
d'
e'
c'
4
5
°
a
b
c
e
d
6
0
°

21. Example 4:
A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of the
pentagon is parallel to the H.P. and 30 mm above it and also inclined at 60o to the V.P. Draw
its projections.
y
x
a'
d'
e'
c'
b'
a
b
c
d
e
30
b'
a'
d'
e'
c'
4
5
°
a
b
c
e
d
6
0
°
a
b

22. Example 4:
A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of the
pentagon is parallel to the H.P. and 30 mm above it and also inclined at 60o to the V.P. Draw
its projections.
y
x
a'
d'
e'
c'
b'
a
b
c
d
e
30
b'
a'
d'
e'
c'
4
5
°
a
b
c
e
d
6
0
°
a
b

23. Example 4:
A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of the
pentagon is parallel to the H.P. and 30 mm above it and also inclined at 60o to the V.P. Draw
its projections.
y
x
a'
d'
e'
c'
b'
a
b
c
d
e
30
b'
a'
d'
e'
c'
4
5
°
a
b
c
e
d
6
0
°
a
b

24. Example 4:
A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of the
pentagon is parallel to the H.P. and 30 mm above it and also inclined at 60o to the V.P. Draw
its projections.
y
x
a'
d'
e'
c'
b'
a
b
c
d
e
30
b'
a'
d'
e'
c'
4
5
°
a
b
c
e
d
6
0
°
a
b
c

25. Example 4:
A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of the
pentagon is parallel to the H.P. and 30 mm above it and also inclined at 60o to the V.P. Draw
its projections.
y
x
a'
d'
e'
c'
b'
a
b
c
d
e
30
b'
a'
d'
e'
c'
4
5
°
a
b
c
e
d
6
0
°
a
b
c
d
e

26. Example 4:
A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of the
pentagon is parallel to the H.P. and 30 mm above it and also inclined at 60o to the V.P. Draw
its projections.
y
x
a'
d'
e'
c'
b'
a
b
c
d
e
30
b'
a'
d'
e'
c'
4
5
°
a
b
c
e
d
6
0
°
a
b
c
d
e

27. Example 4:
A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of the
pentagon is parallel to the H.P. and 30 mm above it and also inclined at 60o to the V.P. Draw
its projections.
y
x
a'
d'
e'
c'
b'
a
b
c
d
e
30
b'
a'
d'
e'
c'
4
5
°
a
b
c
e
d
6
0
°
a
b
c
d
e

28. Example 4:
A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of the
pentagon is parallel to the H.P. and 30 mm above it and also inclined at 60o to the V.P. Draw
its projections.
y
x
a'
d'
e'
c'
b'
a
b
c
d
e
30
b'
a'
d'
e'
c'
4
5
°
a
b
c
e
d
6
0
°
a
b
c
d
e

29. Example 4:
A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of the
pentagon is parallel to the H.P. and 30 mm above it and also inclined at 60o to the V.P. Draw
its projections.
y
x
a'
d'
e'
c'
b'
a
b
c
d
e
30
b'
a'
d'
e'
c'
4
5
°
a
b
c
e
d
6
0
°
a
b
c
d
e
a'
b'
c' e'
d'

30. Example 4:
A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of the
pentagon is parallel to the H.P. and 30 mm above it and also inclined at 60o to the V.P. Draw
its projections.
y
x
a'
d'
e'
c'
b'
a
b
c
d
e
30
b'
a'
d'
e'
c'
4
5
°
a
b
c
e
d
6
0
°
a
b
c
d
e
a'
b'
c' e'
d'

32. Example 5:
A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of the
pentagon is parallel to the H.P. and 30 mm above it. The top view of the line joining the mid-
point of the parallel side to the opposite corner is inclined at 30o to the V.P. Draw its
projections.

33. Example 5:
A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of the
pentagon is parallel to the H.P. and 30 mm above it. The top view of the line joining the mid-
point of the parallel side to the opposite corner is inclined at 30o to the V.P. Draw its
projections.
y
x
a'
d'
e'
c'
b'
a
b
c
d
e
30
b'
a'
d'
e'
c'
4
5
°
a
b
c
e
d

34. Example 5:
A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of the
pentagon is parallel to the H.P. and 30 mm above it. The top view of the line joining the mid-
point of the parallel side to the opposite corner is inclined at 30o to the V.P. Draw its
projections.
y
x
a'
d'
e'
c'
b'
a
b
c
d
e
30
b'
a'
d'
e'
c'
4
5
°
a
b
c
e
d
m
m'
m
m'

35. Example 5:
A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of the
pentagon is parallel to the H.P. and 30 mm above it. The top view of the line joining the mid-
point of the parallel side to the opposite corner is inclined at 30o to the V.P. Draw its
projections.
y
x
a'
d'
e'
c'
b'
a
b
c
d
e
30
b'
a'
d'
e'
c'
4
5
°
a
b
c
e
d
m
m'
m
m'
3
0
°

36. Example 5:
A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of the
pentagon is parallel to the H.P. and 30 mm above it. The top view of the line joining the mid-
point of the parallel side to the opposite corner is inclined at 30o to the V.P. Draw its
projections.
y
x
a'
d'
e'
c'
b'
a
b
c
d
e
30
b'
a'
d'
e'
c'
4
5
°
a
b
c
e
d
d
m
m'
m
m'
m
3
0
°

37. Example 5:
A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of the
pentagon is parallel to the H.P. and 30 mm above it. The top view of the line joining the mid-
point of the parallel side to the opposite corner is inclined at 30o to the V.P. Draw its
projections.
y
x
a'
d'
e'
c'
b'
a
b
c
d
e
30
b'
a'
d'
e'
c'
4
5
°
a
b
c
e
d
a
b
d
m
m'
m
m'
m
3
0
°

38. Example 5:
A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of the
pentagon is parallel to the H.P. and 30 mm above it. The top view of the line joining the mid-
point of the parallel side to the opposite corner is inclined at 30o to the V.P. Draw its
projections.
y
x
a'
d'
e'
c'
b'
a
b
c
d
e
30
b'
a'
d'
e'
c'
4
5
°
a
b
c
e
d
a
b
c
d
e
m
m'
m
m'
m
3
0
°

39. Example 5:
A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of the
pentagon is parallel to the H.P. and 30 mm above it. The top view of the line joining the mid-
point of the parallel side to the opposite corner is inclined at 30o to the V.P. Draw its
projections.
y
x
a'
d'
e'
c'
b'
a
b
c
d
e
30
b'
a'
d'
e'
c'
4
5
°
a
b
c
e
d
a
b
c
d
e
m
m'
m
m'
m
3
0
°

40. Example 5:
A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of the
pentagon is parallel to the H.P. and 30 mm above it. The top view of the line joining the mid-
point of the parallel side to the opposite corner is inclined at 30o to the V.P. Draw its
projections.
y
x
a'
d'
e'
c'
b'
a
b
c
d
e
30
b'
a'
d'
e'
c'
4
5
°
a
b
c
e
d
a
b
c
d
e
m
m'
m
m'
m
3
0
°

41. Example 5:
A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of the
pentagon is parallel to the H.P. and 30 mm above it. The top view of the line joining the mid-
point of the parallel side to the opposite corner is inclined at 30o to the V.P. Draw its
projections.
y
x
a'
d'
e'
c'
b'
a
b
c
d
e
30
b'
a'
d'
e'
c'
4
5
°
a
b
c
e
d
a
b
c
d
e
a'
b'
c' e'
d'
m
m'
m
m'
m
3
0
°

42. Example 5:
A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of the
pentagon is parallel to the H.P. and 30 mm above it. The top view of the line joining the mid-
point of the parallel side to the opposite corner is inclined at 30o to the V.P. Draw its
projections.
y
x
a'
d'
e'
c'
b'
a
b
c
d
e
30
b'
a'
d'
e'
c'
4
5
°
a
b
c
e
d
a
b
c
d
e
a'
b'
c' e'
d'
m
m'
m
m'
m
3
0
°

43. Example 5:
A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of the
pentagon is parallel to the H.P. and 30 mm above it. The top view of the line joining the mid-
point of the parallel side to the opposite corner is inclined at 30o to the V.P. Draw its
projections.
y
x
a'
d'
e'
c'
b'
a
b
c
d
e
30
b'
a'
d'
e'
c'
4
5
°
a
b
c
e
d
a
b
c
d
e
a'
b'
c' e'
d'
m
m'
m
m'
m
3
0
°
m'

44. Example 5:
A regular pentagon of 50 mm side has its surface inclined to the H.P. at 45o. One side of the
pentagon is parallel to the H.P. and 30 mm above it. The top view of the line joining the mid-
point of the parallel side to the opposite corner is inclined at 30o to the V.P. Draw its
projections.
y
x
a'
d'
e'
c'
b'
a
b
c
d
e
30
b'
a'
d'
e'
c'
4
5
°
a
b
c
e
d
a
b
c
d
e
a'
b'
c' e'
d'
m
m'
m
m'
m
3
0
°
m'