Projections of planes.pptx

Types of Planes
• On the basis of position with respect to reference
planes
• Perpendicular to both the reference planes
• Perpendicular to one plane and parallel to the other
• Perpendicular to one plane and inclined to the other
Perpendicular planes
• Inclined to both the reference planes
Oblique planes
1
SBT
08-Jul-09

Projections of different positions
of planes
• FV and TV (both edge views) are obtained in straight line
perpendicular to x-y line
• FV  Coincide with Vertical trace (VT)
• TV  Coincide with Horizontal trace (HT)
Perpendicular to both ref. planes
VP
HP
Square
plate x y
FV
TV
2
SBT
08-Jul-09

Plane perpendicular to one plane and parallel to other
• Plane perpendicular to HP and parallel to VP
• Plane perpendicular to VP and parallel to HP
• FV shows true shape of plane
• TV shows edge view (line parallel to x-y line) of plane
A. Plane perpendicular to HP and parallel to VP
• TV shows true shape of plane
• FV shows edge view (line parallel to x-y line) of plane
B. Plane perpendicular to VP and parallel to HP
x x
y y
FV
TV
Edge view
Edge view
FV
TV
True shape
True shape
3
SBT
08-Jul-09

08-Jul-09 SBT 4
y
HP
VP
x
a
b
c
b’ c’
a’
5
10
45˚
Plane parallel to one plane and perpendicular to other plane: Illustrative Examples
Plane: equilateral triangle
Surface: parallel to HP &
perpendicular to VP
Position: corner A is 5 mm
away from VP & edge AB
makes angle of 45˚ with VP
Plane: regular pentagon
Surface: in VP
Position: edge AB
perpendicular to HP
a’
b’
c’
d’
e’
b
a e
c
d
Plane: square
Surface: parallel to VP and
10 mm from VP
Position: corner B is in HP
& edge BA & BC equally
inclined at 45˚ with HP
b’
a’ c’
d’
10
a b
d
c
45˚

08-Jul-09 SBT 5
y
HP
VP
x
Plane parallel to one plane and perpendicular to other plane: Illustrative Examples
Plane: regular hexagon
Surface: parallel to & 5
mm above HP
Position: corner F is 10 mm
from VP and edge AB & DE
are perpendicular to VP
10
f
a
b
c
d
e
5
a’
b’
f’
c’
e’
d’
Plane: regular pentagon
Surface: parallel to & 10
mm above HP
Position: corner A in VP &
edge AE makes an angle of
30˚ with VP
30˚
a
e
b
c
d
10
b’ c’ d’ e’
a’
Plane: circle of dia. 40 mm
Surface: in VP
Position: centre is 25 mm
above HP
25
1’
2’
3’
4’
1
4
3
2

Plane perpendicular to one plane and inclined to other
• A. Plane perpendicular to VP and inclined to HP
• B. Plane perpendicular to HP and inclined to VP
6
SBT
08-Jul-09

Initially plane is
resting on HP
OR llel to HP
TV1
FV1
Initially plane is
llel to VP
TV
FV FV
TV
TV
FV FV
TV
FV1
FV1
FV2
FV2
x y
x y
Reorient
previous FV
Reorient
previous TV
FV 2
TV 2
start
start end
end
7
SBT
08-Jul-09

y
HP
VP
x
Plane perpendicular to one plane and inclined to other plane: Illustrative Examples
1. A rectangle of side 20 mm and 40 mm is having shorter edge parallel to VP and
surface is perpendicular to HP inclined at angle 30˚ with VP
Initially plane is assumed to be parallel
to VP. The FV of plane is drawn first
showing true shape & size of the plane
with shorter edge is perpendicular to xy
Stage I
a’
b’ c c’
d’
a
b
d
c
In next stage plane making 30˚ with
VP. Corresponding projection is
obtained by reorienting the earlier
TV at 30˚ with xy
a
b
d
c
a’ d’
b’ c’
30˚
Then , obtain corresponding
TV i.e. edge view (line)
parallel to xy
Stage II
Then , obtain
corresponding TV which
shows an apparent shape
& size of plane
20
50

y
VP
x
Initially plane is assumed to be parallel
to VP. The FV of plane is drawn first
showing true shape & size of the plane
with shorter edge is perpendicular to xy
Stage I
a’
b’ c c’
d’
a
b
d
c
TV i.e. edge view (line)
parallel to xy
20
50
2. A rectangle of 20 and 40 mm side is so placed that its surface is perpendicular to HP
and inclined to VP at such an angle that FV of plane appears to be a square of 20 mm
sides. Draw projection and fined out the angle of surface with VP.
Stage II
In next stage plane is
inclined to VP at such an
angle that FV appears to be
a square of 20 mm side
a’ d’
b’ c’
a
b
d
c
20
δ = 60˚
TV (edge view) having same
length of earlier TV as shown
in coming step and measure
angle δ
HP

y
VP
x
3. A regular hexagon of 20 mm side is having as edge in VP and surface is perpendicular
to HP and makes 30˚ with VP.
HP
f’
a’
b’
c’
e’
a
b
f
c
e
d b
a
d
30˚
e
c
f
f’
a’ e’
b’
d’
d’
c’
Initially it is assumed plane is in VP. The
FV of plane is drawn first showing true
shape & size of the plane with one edge
is perpendicular to xy
TV i.e. edge view (line) on
xy
TV at 30˚ with xy
Then , obtain
& size of plane
Stage I Stage II

y
VP
x
4. A regular hexagon of 20 mm edges is having a corner in VP and surface is
perpendicular to HP and makes 30˚ with VP.
HP
a’
b’
e’
f’
a
f
b
e
c d a 30˚
d
c
e
b
f
f’ e’
a’
d’ d’
b’
c’
c’
is parallel to xy
xy
VP with a corner is on VP
Corresponding projection is
TV at 30˚ with xy with pt ‘a’ on xy
Stage I Stage II
Then , obtain
corresponding FV which
& size of plane

y
HP
VP
x
5. A rectangle of side 20 mm and 40 mm is having shorter edge parallel to VP and
surface is perpendicular to HP inclined at angle 30˚ with VP
a
b
c
d
e
108˚
a’
e’
b’
d’ c’
Stage I
xy
a’
e’
d’
d
b’
40˚
c’
e
c
a
b
Then , obtain
& size of plane
Initially it is assumed plane is in HP. The
TV of plane is drawn first showing true
is perpendicular to xy
Stage II
HP with an edge is on HP.
FV at 40˚ with xy with pt a’ & e’ on
xy

y
HP
VP
x
6. A regular pentagon having a corner in HP and surface is perpendicular to VP and
inclined at 40˚ with HP.
b
c
d
a’
b’
e’ c’
e
d’
a
Initially it is assumed plane is in HP. The
TV of plane is drawn first showing true
shape & size of the plane with one edge is
perpendicular to xy (set farthest corner
of this edge on RHS )
Stage I
a’
e’
b’
40˚
c’
xy
Stage II
HP with an edge is on HP.
FV at 40˚ with xy with pt a’ & e’ on
xy
e
d
d’
a
b
c
Then , obtain
& size of plane

y
HP
VP
x
7. A circle of 40 mm diameter is having its surface perpendicular to VP and inclined at
45˚ with HP.
2
4
6
8
10
1’
2’ 3’ 4’ 5’ 6’
7’
8’
9’
10’
11’
12’
1’
7
7’
10’
4’
11’
12’
9’
5’
6’
8’
3’
2’
10
11 9
12 8
1 7
2 6
3 5
4
45˚
Stage I Stage II
1
3
5
12
11 9

y
HP
VP
x
8. A circle of 40 mm diameter is so placed that its surface is perpendicular to VP and is
inclined to HP such a manner that is TV appears to be an ellipse of 40 mm major axis and
30 mm minor axis. Draw the projection and find out the angle of surface of plane with HP.
2
4
6
8
10
1’
2’ 3’ 4’ 5’ 6’
7’
8’
9’
10’
11’
12’
1’
7
7’
10’
4’
11’
12’
9’
5’
6’
8’
3’
2’
10
11 9
12 8
1 7
2 6
3 5
4
45˚
Stage I Stage II
1
3
5
12
11 9

y
VP
x
3. (Q.14 Pg.21) A thin 45⁰ set square has its longest side 250 mm long in VP and
inclined at 30⁰ to HP. Its surface makes an angle of 45⁰ with VP. Draw projections.
(W-2003, 7 marks)
HP
a’
b’
45˚
a
b c
a
b
c
a’
c’
c’
b’
a’
c’
b’
a’
c’
b’
a’
c’
b’
30˚
a b
c
Initially it is assumed plane is in VP.
The FV of plane is drawn first showing
true shape & size of the plane with
longest edge is perpendicular to xy
Stage I
xy In next stage plane making 45˚ with
VP with a longest edge is in VP.
Corresponding projection is obtained
by reorienting the earlier TV at 45˚
with xy with pt. ‘a’ & ’b’ on xy
Stage II
In last stage longest edge of plane
which is in VP making 30˚ with HP.
by reorienting the earlier FV in such a
manner that FV of the above
mentioned edge makes 30˚ with xy .
Stage III
Then , obtain
corresponding final TV .
45˚
Then , obtain
corresponding FV which
& size of plane

x
3. A 30⁰ - 60⁰ triangle PQR has its longest side PR is 50 mm long and is contained in VP.
P and R are 20 mm and 45 mm respectively from HP, while point Q is 10 mm away from
VP. Draw projection. (W – 92, 7 marks)
20
VP
HP
30˚
60˚
p’
r’
p
r
q
xy
In next stage pt. Q is 10 mm away
from VP with longest edge (PR) is in
obtained by reorienting the earlier TV
in such a manner pt. ‘q’ 10 mm below
xy
10
p
r
shape & size of the plane with longest
edge PQ is perpendicular to xy and at
given position with respect to xy
Stage I
p’
q’
q’
r’
In last stage longest edge of plane
which is in VP making 30˚ with HP.
by reorienting the earlier FV in such a
manner that FV of the above
mentioned edge makes 30˚ with xy .
Stage III
Stage II
p’
q’
r’
20
r’
45
p’
q’
20
p’
Then , obtain
corresponding final TV .
r P
q
q’
y

y
x
3. A 30⁰ - 60⁰ - 90⁰ set square is having its surface making an angle of 45⁰ with HP and
is having its longer edge PQ which is 125 mm long is in HP and making an angle of 30⁰
with VP.
HP
30˚
60˚
p
r’
VP p’
q’
p’
q’
45˚
r’
p
r r
q q
p
r
q
30˚
p
r
q
p’ q’
r’

y
x
3. A thin triangular plane PQR has sides PQ 60 mm, QR = 80 mm and RP = 50
respectively. Side PQ rests on ground and makes an angle of 30⁰ with VP. Point P is 20
mm away from VP and point R is 40 mm above ground. Draw projection of plane.
p
q
r
60
p’
q’
r’
40
p’
q’
r’
r
p
q
r
p
q
20
r
p
q
30˚
r’
q’ p’

Plane perpendicular to one plane and inclined to other
• A. Plane perpendicular to VP and inclined to HP
• B. Plane perpendicular to HP and inclined to VP
• Projection is obtained in TWO stages
• In first stage, initially plane is consider to be llel to HP with given
edge condition and obtain TV (true shape) and then
corresponding FV (edge view)
• In next stage, previous FV is reoriented at given angle and
corresponding TV is obtained
A. Plane perpendicular to VP and inclined to HP
• Projection is obtained in TWO stages
• In first stage, initially plane is consider to be llel to VP with
given edge condition and obtain FV (true shape) and then
corresponding TV (edge view)
• In next stage previous TV is reoriented at given angle and
corresponding FV is obtained
B. Plane perpendicular to HP and inclined to VP
20
SBT
08-Jul-09

Plane inclined to both the plane (Oblique plane)
• A. Plane is inclined to HP with edge or dia. or diagonal is llel to HP
and inclined to VP
• B. Plane is inclined to VP with edge or dia. or diagonal is llel to VP
and inclined to HP
21
SBT
08-Jul-09

A. Plane is inclined to HP with edge or diameter
or diagonal is llel to HP and inclined to VP
TV
FV FV
TV
start
TV
FV
end
22
SBT
08-Jul-09
Initially plane is
resting on HP
OR llel to HP
FV1
FV2
x
y
Reorient
previous FV
Reorient
previous edge
FV1
TV 3
TV 2
FV 3
θ˚
φ˚

B. Plane is inclined to VP with edge or diameter
or diagonal is llel to VP and inclined to HP
FV1
x y
Initially plane is
llel to VP
Reorient
previous TV
Reorient
previous FV
TV
FV FV
TV
start
TV
FV
end
TV1
23
SBT
08-Jul-09
φ˚
θ˚
FV 2 FV3
FV3
TV2

x y
HP
VP
b’
a’
108˚
d’
c’
e’
b
a
c
e
d b
a
45
d
c
e
e’
a’
b’
c’
d’
e’
a’
b’
c’
d’
45˚
e’
b’
c’
d’
e’
b’
c’
d’
a b
e c
d
3. A pentagonal plane ABCDE of side 35 mm has its side AB in VP an inclined at 45⁰ to HP.
Draw projection when opposite corner to that edge is 45 mm in front of VP.

x y
HP
VP
a
b
c
d
e
108˚
a’
e’
b’
d’ c’
a’
e’
c’
b’
d’
a
b
c
d
e
a
b
c
d
e
a
d
e
c
b
a’ e’
b’
d’
c’
30˚
60˚
60˚
b’
c’
d’
e’
a’

y
x
3. A plate having shape of isosceles triangle has base 50 mm long and altitude 75 mm.
It is so placed that in Front View it is seen as an equilateral triangle of 50 mm sides and
one side inclined at 45⁰ to xy. Draw its Top View.
HP
VP
a
b c
a’ a’
b’
c’ c’
a
b
c
δ
a’
b’
c’
a’
b’
c’
a’
b’
c’
45˚
a b
c
b’

y
x
3. A thin rectangular plate of size 70 mm X 40 mm appears as a square of 40 mm sides
in TV with one of its sides inclined at 30⁰ to VP and parallel to HP. Draw the projections
of plate and determine its inclined with HP.
HP
VP
70
40
a
b c
d
a’
b’
d’
c’
a
b c
d
a’
b’
d’
c’
γ
30˚
b
c
d
a
40
40
b’ a’
c’ d’

y
x
3. A 30⁰ - 60⁰ set square has its shortest side 40 mm long in HP. TV of set square is an
isosceles triangle. Draw projection of plane and find its inclination with HP.
HP
VP
60˚
a
b
c
a’
b’
c’
a
b
c
a’
b’
c’
γ

y
x
3. A The TV of a 45⁰ set square with side BC in HP and side AB in VP, is a triangle abc.
The side bc = 20 mm being perpendicular to xy and angle bca = 25⁰. Draw TV and FV
and measure the inclination of set square with HP. Draw also Side View.
HP
VP
b
c
a
45˚
b
c
25˚
a
b’c’ a’ b’c’
a’
γ
x1
y1
c’’
b’’
a’’

08-Jul-09 SBT 30
x y
1
2
3
4
5
6
8
10
11
12
HP
VP 1’
2’ 3’ 4’ 5’ 6’
7’
8’
9’
10’
11’
12’
1’
7
9
7’
10’
4’
11’
12’
9’
5’
6’
8’
3’
2’
10
11 9
12 8
1 7
2 6
3 5
4
45˚
1
7
4
10
2
6
12
8
11
9
3
5
1’
2’ 12’
3’
11’
4’
10’
5’
9’
6’
8’
7’
60˚
30˚
Reorient FV1 i.e. edge view
at an angle of 45°
Reorient TV2 so that TV2 of
diagonal AB (a’b’) at an angle
of 45°
Stage I Stage II Stage III
3. A circle of 40 mm diameter is having its surface making an angle of 45⁰ with HP and end A of
diameter AB is in HP and TV of diameter AB makes an angle of 30⁰ with VP. Draw projections.

08-Jul-09 SBT 31
x y
1
2
3
4
5
6
8
10
11
12
HP
VP 1’
2’ 3’ 4’ 5’ 6’
7’
8’
9’
10’
11’
12’
1’
7
9
7’
10’
4’
11’
12’
9’
5’
6’
8’
3’
2’
10
11 9
12 8
1 7
2 6
3 5
4
45˚
30˚
a
b
b1
β˚
1
7
4
10
3
5
11
9
2
6
12
8
1’
2’ 12’
3’
4’
5’
6’
7’
8’
9’
10’
11’
Reorient FV1 i.e. edge view
at an angle of 45°
Reorient TV2 so that TV2 of
diagonal AB (a’b’) at an angle
of 45°
Stage I Stage II Stage III
3. A circle of 40 mm diameter is having its surface making an angle of 45⁰ with HP and end A of
diameter AB is in HP and diameter AB makes an angle of 30⁰ with VP. Draw projections.

08-Jul-09 SBT 32
x
y
VP
2’
4’
5’
6’
7’
7’
7’
6’
5’
4’
3’
2’
1’
7’
6’ 5’
4’
3’
2’
1’
45˚
7 1
6 2
5 3
7’
6’
5’
4’
3’
2’
1’
3’
1’
HP
1’
7’
6’
2’
5’
3’
4’
1
6
3
5’
2
4

x
y
3. A rhombus of diagonal 125 mm and 50 mm is so placed that it appears as a square of 50 mm
diagonal in TV. The smaller diagonal of rhombus is parallel to both HP and VP.
HP
VP
b
d
a’
b’
d’ c’
d
b
a
a c c
a’
b’
d
b
a c
c
a
d b
a’
d’ b’
c’
d’
c’

08-Jul-09
x
y
3. A equilateral triangle ABC having side length as 50 mm is suspended from a point O on side AB
15 mm from A in such a way that plane of triangle makes an angle of 60⁰ with VP. Point O is 50 mm
above HP and 40 mm in front of VP. Draw projection of triangle.
a’
HP b’
60˚
40
b a c
50
g’
o’
VP
c’
a’
b’
g’
o’
c’
50
a’
b’ 50
g’
o’
c’
a’
b’
g’
o’
50
c’
a
b c
o
g
b
c
o
g
a
60˚
b’
c’
a’

08-Jul-09 SBT 35
x
y
VP 2’
4’
5’
6’
7’
3’
1’
HP
3. A semicircle having diameter 100 mm is suspended from a point ‘O’ on straight edge 30 mm
from centre of that edge so that the surface makes an angle of 45⁰ with VP. Point ‘O’ is 90 mm
above HP and 50 mm in front of VP. Draw projections. (W – 05, 7 marks)
m’ g’
o’
1
7
6
2
5
3
4
m g
o
50
2’
5’
6’
7’
3’
1’
m’ g’
o’
90
2’
5’
6’
7’
3’
1’
m’
g’
o’
90
2’
5’
6’
7’
3’
1’
m’
g’
o’
30
4’
1 2 3 4 5
6
7
g
o
m
1
4
5
6
2
3
7
g
o
m
45˚
1’
2’
3’
4’
5’
6’
7’

x y
HP
VP
c
d
d
b
a
c
d
e
d
e
b
a

x y
HP
VP
a’
b’
c’
d’
e’
f’
b
a
c
f
d
e
40˚
b
a
c
f
d
e
b’ d’
c’
a’ e’
f’
b’ d’
c’
a’ e’
f’
b’
c’
a’
e’
f’
30˚
b’
c’
a’
e’
f’
a b
c
f
e d
3. A regular hexagon of 30 mm edge is having its surface inclined at 40⁰ with VP and is
having an edge in VP and inclined at an angle 30⁰ with HP. Draw projections.

x y
HP
VP
a’
b’
c’
d’
e’
f’
b
a
c
f
d
e
δ
b
a
c
f
d
e
b’ d’
c’
a’ e’
f’
b’ d’
c’
a’ e’
f’
b’
c’
a’
e’
f’
30˚
b’
c’
a’
e’
f’
a b
c
f
e d
3. One side of a regular hexagon of 30 mm side is in VP, while opposite side is 35 mm
in front of VP and inclined at 30⁰ to HP. Draw projection of plane and find its surface
inclination with VP.
35

x HP
VP
a’
b’
c’
d’
e’
f’
b
a
c
f
d
e
40˚
b
a
c
f
d
e
b’ d’
c’
a’ e’
f’
30˚
x1
y1
a
b
c
d
e
f

x y
HP
VP
c
e
f
a
f
c
e
d
b
40˚
d
f
f’ e’
b’ c’
f’ e’
a’ d’
b’ c’
f’
a’
d’
b’
c’
f’
b’
30˚
a’
d’
c’
a
f b
e c
d
b
e
c
a d a’ d’
3. A regular hexagon of 25 mm edge is having its surface making an angle of 40⁰ with
VP and is having a corner in VP. The FV of diagonal containing this corner makes an
angle of 30⁰ with HP. Draw the projections.
b a

x HP
VP
c
e
f
a b
f
c
e
d
b
40˚
a
d
f
f’ e’
b’ c’
f’ e’
a’ d’
b’ c’
30˚
b
e
c
d’ a’ d’
3. A regular hexagon of 25 mm edge is having its surface making an angle of 40⁰ with
VP and is having a corner in VP. The diagonal containing this corner makes an angle of
30⁰ with HP. Draw the projections.
d1’
d’
α
f’
e’
b’
c’
a’
a
f
b
e c
d

x y
c
e
f
a’ b’ c’
e’
d’
a d
b
a’
d’
b’
35˚
f e
a d
b c
f
e
a
d
b
c
f
a
d
b
c
e’
f’ b’
a’
x1
y1
a’’
f’’
e’’
d’’
3. A hexagonal plane ABCDEF of side30 mm has corner A in HP and opposite corner D
in VP. Draw three views o plane when diagonal AD inclined at 35⁰ to HP and parallel to
profile plane. Determine its surface inclination with VP.
e
c’ c’’
c’
e’
f’
f’
b’’
d’

x y
HP
VP
3. A thin pentagonal plate of negligible thickness and sides 25 mm long having one of
its corner in VP and surface makes an angle of 30⁰ with VP and side opposite to that
corner makes an angle of 60⁰ with HP. Draw its projection. (S – 2005)
d’
c’
108˚
a’
e’
b’
a b
e
c
d
30˚
a
c
d
b
e
e’
d’
a’
b’
c’
e’
d’
a’
b’
c’
d’
a’
b’
c’
60˚
a
b
e
c d

y
3. A composite plane consist of square ABCD of 75 mm sides and a semi circle along
CD as diameter. Draw the TV and FV of plane if its surface is perpendicular to HP and
makes an angle of 45⁰ with VP. Then draw auxiliary view on an AIP which makes an
angle of 30⁰ with edge AB which is perpendicular to HP.
6’
3’
2’
1’
5’
7’
a’
b’
4’
d’
c’
a
b
d
c
1
7
2
6
3
5
4
a
b
d
c 1
7
6
3
5
4
a’ d’
3’
4’
b’ c’ 7’
45˚
x1
b1’
7’
d1’
1’
2’
3’
4’
4’
c1’
6’
5’
6’
y1
2’
1’
a1’

x y
HP
VP
a
108˚
c
e
b’
a’
c
e
d b’
a’
5. A A thin regular pentagonal plate of 60 mm long edge has one of its edge in the HP
and perpendicular to VP, while its farthest corner is 60 mm above HP. Draw projection
of plate. Project another FV on an AVP making angle of 45⁰ with VP. Also project an
auxiliary view (ATV) of the same plane on and AIP which makes an angle of 60⁰ with HP.
60
d’
c’
e’
d
d
b b
c
e
a
x1
y1
60˚
a1
b1
e1
c1
d1
30˚
x2
y2
a1’
b1’
c1’ d1’
e1’

3. Determine a true shape of a plane where surface is perpendicular to VP and is
inclined at an angle of 45⁰ with HP and whose TV is a regular pentagon of 30 mm sides
with one side making an angle of 30⁰ with xy line in TV.
x y
HP
VP
108˚
a
c
b
d
30˚
e
a’
b’
e’
d’
c’
45˚
x2
y2
b1’
c1’
a’
d1’
e1’

3. abc is an equilateral triangle of altitude 50 mm with ab in xy and c bellow xy. abc’ is
an isosceles triangle of altitude 75 mm and c’ above xy. Determine the true shape of
triangle of ABC of which abc is TV and abc’ is FV.
x HP
VP
30˚
30˚
50
a b
c
c’
75
x1
y1
a’’
b’’
c’’
δ
γ
x2
y2
b2
a2
c2
y

3. The FV and TV of a plane is squares of 40 mm sides, with two sides equally inclined to xy.
Draw the true shape of the plane. Also determine the inclined angle between the sides.
x HP
VP
y
b’
d’
b
45˚ 45˚
c
d
x1
y1
b’’
a
c’
a’
a’’
c’’
d’’
γ
45˚ 45˚
δ
x2
y2
a2
b2
c2
d2

3. Lines AB and AC appears to make an angle of 120⁰ between them in their FV and TV line
AB is parallel to both the plane. Assume suitable view length. Determine the real angle
between lines AB and AC.
x y
HP
VP
a’
b’
c’
120˚
b
a
c
120˚
x1
y1
a’’
b’’
c’’
x2
y2
a2
b2
c2
ψ = 112⁰

x y
HP
3. The A picture frame 2 m wide and 1 mm high is to be fixed on a wall railing by two
straight wires attached to the top corner. The frame is to make an angle of 40⁰ with the
wall and the wires are to be fixed to a hook on a wall on center line of frame and 1.5 m
above railing. Find the length of wires and angles between them.
x1
y1
40˚
a’
b’ c’
d’
c’’
a’’
d’’
h’ h’’
b’’
1.5
m
a d
VP b c
2 m
h
x2
h2
a2
ψ = 91⁰
d2
y2

3. An isosceles triangle ABC is having its corners A, B and C respectively 30 mm, 60 mm and
90 mm in front of VP. Draw projection of plane and determine its surface inclination with
HP and VP. Take base of triangle AB equal to 60 mm and altitude equal to 90 mm .
x y
HP
VP
30
30
b
a
b
ci
a
b’ a’ ci’
30
c
c
x1
y1
a1’
b1’
ci1’
c1
γ = 55⁰
c’

3. An isosceles triangle ABC is having, base 60 mm and altitude 40 mm has its base AC in
HP and inclined at 30° to VP. Corner A and B are in VP. Draw its projection.
x HP
VP
Initially it is assumed ∆ ABC is in HP with pt
A is in VP and edge AC making angle of 30°
with VP. Corresponding projection is
obtained by drawing TV (showing True
Shape ) and corresponding FV (showing
Edge View)
c
30˚
bi
y
x1
y1
c’ bi’
b a
a1’
b1’
bi1’
b1’
γ = 64⁰
b’

3. An isosceles triangle PQR having base PQ 50 mm long and altitude 75 mm has its corner
P, Q and R, 25 mm, 50 mm and 75 mm respectively above ground. Draw its projection.
x HP
VP
y
ri’
r’
30
30
q’
r’
30
p’
x1
y1
q p ri
q’
p’ p1
q1
ri1
r1
γ = 55⁰
r

3. Draw TV and FV of a hexagonal lamina of 30 mm side, having two of the edges parallel to
both HP and VP and the nearest edge is 12 mm from each plane. The surface of lamina is
inclined at 60° to HP.
x y
HP
VP
c
d
e
a
12
b’
a’
c’
d’
d’
e’
b’
a’
d’
e’
d’
d
a e
d
b b d
c
60⁰
12
d
a e
b d
c
d
a
e
b
d
c
d
a
e
c
b
d
d’
d’
c’
a’ b’
x1
y1
a’’
b’’
c’’
d’’
d’’
e’’
e’
c’

Try to understand
P
Q
R
S
A
B
C
D
R
P
30
C
A
60
R C
P A
30 60
Corners P and A on the ground and
plane parallel to VP
Corners P and A on the ground and
plane perpendicular to VP with
corners R and C touches Each other
such that diagonal PR and AC
perpendicular to each other
x = 67
x2 = 302 + 602
3. An PQRS and ABCD are two square planes of diagonals 30 mm and 60 mm respectively
having their corners P and A on ground and corners R and C touches each other. The
surface of both the planes are perpendicular to each other and are perpendicular to VP.
Draw projection of planes and also find out the actual length of the side of square. (In
other words obtained the true shape of each plane.)

3. An PQRS and ABCD are two square planes of diagonals 30 mm and 60 mm respectively
having their corners P and A on ground and corners R and C touches each other. The
surface of both the planes are perpendicular to each other and are perpendicular to VP.
Draw projection of planes and also find out the actual length of the side of square. (In
other words obtained the true shape of each plane.)
HP y
p’ 67 a’
r’ c’
q’
s’ b’
d’
p r
q
s
c
a
b
x1
y1
x VP
c1
b1
a1
d1
x2
y2
r1
s1
q1
p1

a e
108˚
c
b d
a
e
108˚
c
b
d
a
e
108˚
c
b
d

2. A thin 45⁰ set square has its longest side 250 mm long in VP and inclined
at 30⁰ to HP. Its surface makes an angle of 45⁰ with VP. Draw projections.
(W-2003, 7 marks)
3. A 30⁰ - 60⁰ triangle PQR has its longest side PR is 50 mm long and is
contained in VP. P and R are 20 mm and 45 mm respectively from HP, while
point Q is 10 mm away from VP. Draw projection. (W – 92, 7 marks)

a
1
2
3
4
5
6
8
10
11
12
7
9
b c
d
e
f
f
a
b
c
d
e

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