Descriptive Geometry
By: Ameer Tofan
Course Objective
To develop the imagination and logical mathematical sense to solve different
engineering problems specially in mechanical eng. Where the design & manufacturing
of rockets & satellites depends on the principles of descriptive geometry.
Annual System: 30 weeks
Stage: Second
Number of weekly hours: 1hr (Theoretical), 1hr (Practical Part)
Number of units: 3
Week No.
Subject Topics
1
Introduction
2
Theory of projection & projection of point
3
Examples on quadrants & dihedral angles
4-6
Projection of straight line
7-8
Representation of straight line in space
9
Examples on dihedral angles for straight line
10-13
The true length and inclinations of a straight line
14-15
Examples for the true length of straight line
16
17-18
19
Auxiliary plane
Type of auxiliary plane
Using Auxiliary plane to find the true length
20-24
Auxiliary plane application
25-26
Open cylinder and definition
27-28
Open cone and definition
29-30
Cut the cone using Auxiliary plane
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Descriptive Geometry
By: Ameer Tofan
Week Number: 1
Introduction
1. Over view
1.A –Target population:
- For students of second class, Technical college-Baghdad, Engineering
Techniques of Materials, Welding, Dies and Tools, Automotive and
Refrigeration and air conditioning.
- For students of first class, Technical college-Baghdad, Engineering
Techniques of Surveying.
1.B – Rationale:
Introduction, is very important subject to be studied in order to have a
full knowledge for the Descriptive Geometry.
1.C – Central Idea:
 Definition of Descriptive Geometry.
 Importance of Descriptive Geometry.
1.D - Performance Objectives:
At the end of this lecture the student should be able to:
 Define the subject of Descriptive Geometry.
2. Pre test
U
1. Is there any limitation for the space ? ( ) yes ( ) No
2. What do you see in the TV screen 2D or 3D picture.
3. The text
U
We live in a three-dimensional world and we often want to represent this world in
a drawing, a painting or a photography. Now, drawings, paintings and photos are twodimensional. So are, indeed, the images formed in each of our eyes. Seen from two
different points, those images are different. It is our brain that restores a threedimensional view from the two images formed in our eyes. In technical drawing we
must use another procedure. The aim of Descriptive Geometry is to describe the
three-dimensional objects by two-dimensional drawings so as to allow to reconstitute
their original forms.
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Descriptive Geometry
By: Ameer Tofan
4. Quiz
Q1: What is Descriptive Geometry describe.
Q2: Why are we need to represent the 3D shape on 2D plane.
5. Post test
Choose the correct answer
1. In technical drawing we must use:
a) Painting
b) photos
d) another procedure
6. References
U
- (An analytical introduction to Descriptive Geometry), Adrian B. Biran, Oxford,
UK Samples - August 2005
Page 3
Descriptive Geometry
By: Ameer Tofan
Week Number: 2 & 3
Theory of projection & projection of point
1. Over view
1.A –Target population:
- For students of second class, Technical college-Baghdad, Engineering
Techniques of Materials, Welding, Dies and Tools, Automotive and
Refrigeration and air conditioning.
- For students of first class, Technical college-Baghdad, Engineering
Techniques of Surveying.
1.B – Rationale:
Theory of projection & projection of point, is very important subject to be
studied in order to make the base of representation on the plane.
1.C – Central Idea:




Central projection.
Parallel projection.
Orthographic projection.
The two-sheet method of Monge.
1.D - Performance Objectives:
At the end of this lecture the student should be able to:
 Project the point on planes.
2. Pre test
U
1. Is the location of scene influence on projection view ? ( ) yes ( ) No
2. How many the direction of Orthographic projection.
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Descriptive Geometry
By: Ameer Tofan
3. The text
Page 5
Descriptive Geometry
By: Ameer Tofan
Page 6
Descriptive Geometry
By: Ameer Tofan
Examples:
Project the points as the following:
A(5,3) B(-2,6) C(-1,-1) D(0,-4)
4. Quiz
Q1: Write the projection type.
Q2: Project the point(2,1) at the principles plane.
5. Post test
1. The perpendicular trace of point on the plane called …………. .
6. References
- (Descriptive Geometry), Dr. Yousef Nicola, National library-Baghdad 1976
Page 7
Descriptive Geometry
By: Ameer Tofan
Week Number: 4 - 6
Projection of straight line
1. Over view
1.A –Target population:
- For students of second class, Technical college-Baghdad, Engineering
Techniques of Materials, Welding, Dies and Tools, Automotive and
Refrigeration and air conditioning.
- For students of first class, Technical college-Baghdad, Engineering
Techniques of Surveying.
1.B – Rationale:
Projection of straight line, is very important subject to be studied in order
to Project the straight line plane surface.
1.C – Central Idea:
 Projection of straight line.
1.D - Performance Objectives:
At the end of this lecture the student should be able to:
 Draw the Projection of straight line on the principles planes.
2. Pre test
U
1. Project the two points on the principles planes:
P1(2,3) P2(4,1)
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Descriptive Geometry
By: Ameer Tofan
3. The text
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Descriptive Geometry
By: Ameer Tofan
Examples:
Draw the elevation and plane of the straight line for the following:
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Descriptive Geometry
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Descriptive Geometry
By: Ameer Tofan
4. Quiz
Draw the elevation and plane of the straight line for the following:
1. A(1,2) B(4,3) right of A projector distance = 6 cm
2. A(6,3) B(5,4) right of A projector distance = 7 cm
3 A(-5,4) B(2,-1) right of A projector distance = 2 cm
5. Post test
Write the procedure to project the straight line
6. References
- (Descriptive Geometry), Dr. Yousef Nicola , National library-Baghdad 1976
- (An analytical introduction to Descriptive Geometry), Adrian B. Biran, Oxford,
UK Samples - August 2005
Page
12
Descriptive Geometry
By: Ameer Tofan
Week Number: 7 - 8
Representation of straight line in space
1. Over view
1.A –Target population:
- For students of second class, Technical college-Baghdad, Engineering
Techniques of Materials, Welding, Dies and Tools, Automotive and
Refrigeration and air conditioning.
- For students of first class, Technical college-Baghdad, Engineering
Techniques of Surveying.
1.B – Rationale:
Representation of straight line in space, is very important subject to be
studied in order to understand the cases of the line in the space .
1.C – Central Idea:
 Cases of the line in the space.
1.D - Performance Objectives:
At the end of this lecture the student should be able to:
 Imagine the line in the space.
2. Pre test
U
Draw the elevation and plane of the straight line below:
1. A(1,2) B(1,5) projector distance = 0 cm
2. A(6,2) B(3,2) projector distance = 0 cm
3. A(3,0) B(0,4) projector distance = 0 cm
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Descriptive Geometry
By: Ameer Tofan
3. The text
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Descriptive Geometry
By: Ameer Tofan
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Descriptive Geometry
By: Ameer Tofan
4. Quiz
Draw the elevation and plane of the straight lines below and describe its case:
1. A(1,2) B(1,2) right of A projector distance = 5 cm
2. A(0,7) B(7,0) right of A projector distance = 6 cm
5. Post test
Write the cases of the straight line in the space.
6. References
- (Descriptive Geometry), Dr. Yousef Nicola , National library-Baghdad 1976
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Descriptive Geometry
By: Ameer Tofan
Week Number: 9
Examples on dihedral angles for straight line
1. Over view
1.A –Target population:
- For students of second class, Technical college-Baghdad, Engineering
Techniques of Materials, Welding, Dies and Tools, Automotive and
Refrigeration and air conditioning.
- For students of first class, Technical college-Baghdad, Engineering
Techniques of Surveying.
1.B – Rationale:
Examples on dihedral angles for straight line, is very important examples
to be studied in order to exercise for dihedral angles for straight line.
1.C – Central Idea:
 Exercises on dihedral angles for straight line.
1.D - Performance Objectives:
At the end of this lecture the student should be able to:
 Imagine and draw the line in the space.
2. Pre test
U
Draw the elevation and plane of the straight line below:
1. A(-1,2) B(-1,5) projector distance = 3 cm
2. A(-6,-2) B(-3,-2) projector distance = 4 cm
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Descriptive Geometry
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3. The text
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Descriptive Geometry
By: Ameer Tofan
4. Quiz
Draw the elevation and plane of the straight lines below and describe its position:
1. A(-5,2) B(-1,2) right of A projector distance = 5 cm
2. A(2,-7) B(6,-3) right of A projector distance = 6 cm
5. Post test
Explain by drawing the projection of the straight line when:
1. Passes through +V.P and +H.P
2. Passes through +V.P and -H.P
3. Passes through -V.P and +H.P
4. Passes through -V.P and -H.P
6. References
- (Descriptive Geometry), Dr. Yousef Nicola , National library-Baghdad 1976
- (An analytical introduction to Descriptive Geometry), Adrian B. Biran, Oxford,
UK Samples - August 2005
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19
Descriptive Geometry
By: Ameer Tofan
Week Number: 10-13
The true length and inclinations of a straight line
1. Over view
1.A –Target population:
- For students of second class, Technical college-Baghdad, Engineering
Techniques of Materials, Welding, Dies and Tools, Automotive and
Refrigeration and air conditioning.
- For students of first class, Technical college-Baghdad, Engineering
Techniques of Surveying.
1.B – Rationale:
The true length and inclinations of a straight line, is very important subject
to be studied in order to determine the true length and its inclinations.
1.C – Central Idea:
 The true length and inclinations of a straight line.
1.D - Performance Objectives:
At the end of this lecture the student should be able to:
 determine the true length and its inclinations.
2. Pre test
U
Determine the true length and inclinations of a straight line below:
1. A(2,2) B(2,5) projector distance = 0 cm
2. A(6,1) B(3,1) projector distance = 0 cm
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Descriptive Geometry
3. The text
By: Ameer Tofan
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Descriptive Geometry
By: Ameer Tofan
4. Quiz
The straight line AB is placed such that A=(3 , 1) and B=(1, 5) right of A. The
distance of projectors between A & B= 5 cm. The horizontal trace is H(-1,0).
1. draw (scale 1:1) the PLAN & ELEVATION of the line.
2. determine the true length inclinations.
3. determine the inclinations.
5. Post test
Define the symbols below:
α , β , T.L
6. References
- (Descriptive Geometry), Dr. Yousef Nicola , National library-Baghdad 1976
- (An analytical introduction to Descriptive Geometry), Adrian B. Biran, Oxford,
UK Samples - August 2005
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Descriptive Geometry
By: Ameer Tofan
Week Number: 14-15
Examples for the true length of straight line
1. Over view
1.A –Target population:
- For students of second class, Technical college-Baghdad, Engineering
Techniques of Materials, Welding, Dies and Tools, Automotive and
Refrigeration and air conditioning.
- For students of first class, Technical college-Baghdad, Engineering
Techniques of Surveying.
1.B – Rationale:
Examples for the true length of straight line, is very important examples to
determine the true length and its inclinations.
1.C – Central Idea:
 Examples for the true length of straight line.
1.D - Performance Objectives:
At the end of this lecture the student should be able to:
 determine the true length and its inclinations.
2. Pre test
U
Determine the true length and inclinations of a straight line below:
1. A(2,1) B(3,4) right of A projector distance = 3 cm
2. A(4,2) B(3,1) right of A projector distance = 4 cm
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Descriptive Geometry
3. The text
By: Ameer Tofan
***********30 31 32
Example (1): The straight line AB is placed such that A=(2 , 4) and B=(5, 1) left of A.
The distance of projectors between A & B= 6 cm.
1. draw (scale 1:1) the PLAN & ELEVATION of the line.
2. determine the true length.
3. determine the inclinations.
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Descriptive Geometry
By: Ameer Tofan
Example (2): The straight line AB is placed such that A=(6 , 2) and B=(2, 2) left of A.
The distance of projectors between A & B= 8 cm.
1. draw (scale 1:1) the PLAN & ELEVATION of the line.
2. determine the true length.
3. determine the inclinations.
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Descriptive Geometry
By: Ameer Tofan
4. Quiz
The straight line AB is placed such that A=(1.5 , 5) and B=(X b , 2) right of A. The
distance of projectors between A & B= 5 cm. The horizontal trace is H(-1,0).
1. draw (scale 1:1) the PLAN & ELEVATION of the line.
2. determine the coordinates X b .
3. determine the inclinations.
4. determine the true length.
5. Post test
Writ the procedures to determine the true length and its inclinations.
6. References
- (Descriptive Geometry), Dr. Yousef Nicola , National library-Baghdad 1976
- (An analytical introduction to Descriptive Geometry), Adrian B. Biran, Oxford,
UK Samples - August 2005
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Descriptive Geometry
By: Ameer Tofan
Week Number: 16 - 18
Auxiliary plane
1. Over view
1.A –Target population:
- For students of second class, Technical college-Baghdad, Engineering
Techniques of Materials, Welding, Dies and Tools, Automotive and
Refrigeration and air conditioning.
- For students of first class, Technical college-Baghdad, Engineering
Techniques of Surveying.
1.B – Rationale:
Auxiliary plane, is very important subject to be studied in order to use the
Auxiliary plane .
1.C – Central Idea:
 Auxiliary plane in the space with respect to the both V.P & H.P.
1.D - Performance Objectives:
At the end of this lecture the student should be able to:
 determine the Auxiliary plane in the space with respect to the both V.P & H.P.
2. Pre test
U
Are we need to project on the another plane with the V.P& H.P ?
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Descriptive Geometry
3. The text
By: Ameer Tofan
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4. Quiz
Write the positions of the Auxiliary plane in the space with respect to the principles
planes of projections.
5. Post test
Write the less importance positions of the Auxiliary plane in the space with respect to
the principles planes of projections.
6. References
- (Descriptive Geometry), Dr. Yousef Nicola , National library-Baghdad 1976
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Descriptive Geometry
By: Ameer Tofan
Week Number: 19
Using Auxiliary plane to find the true length
1. Over view
1.A –Target population:
- For students of second class, Technical college-Baghdad, Engineering
Techniques of Materials, Welding, Dies and Tools, Automotive and
Refrigeration and air conditioning.
- For students of first class, Technical college-Baghdad, Engineering
Techniques of Surveying.
1.B – Rationale:
Using Auxiliary plane to find the true length, is very important subject to
be studied in order to apply the Auxiliary plane to determine the true length.
1.C – Central Idea:
 Apply the Auxiliary plane to determine the true length.
1.D - Performance Objectives:
At the end of this lecture the student should be able to:
 use the Auxiliary plane to determine the true length.
2. Pre test
U
Determine the auxiliary plane which is parallel the to the line A(2,2), B(3,4) right of
A and projector distance = 5 cm.
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3. The text
By: Ameer Tofan
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Descriptive Geometry
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4. Quiz
Use the Auxiliary plane to determine the true length of the line A(2,1), B(4,2) right
of A and projector distance = 5 cm.
5. Post test
Writ the procedures to use the Auxiliary plane to determine the true length of the line .
6. References
- (Descriptive Geometry), Dr. Yousef Nicola , National library-Baghdad 1976
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Descriptive Geometry
By: Ameer Tofan
Week Number: 20-24
Auxiliary plane application
1. Over view
1.A –Target population:
- For students of second class, Technical college-Baghdad, Engineering
Techniques of Materials, Welding, Dies and Tools, Automotive and
Refrigeration and air conditioning.
- For students of first class, Technical college-Baghdad, Engineering
Techniques of Surveying.
1.B – Rationale:
Auxiliary plane application, is very important subject to be studied in
order to apply the Auxiliary plane to project the plane shapes.
1.C – Central Idea:
 Apply the Auxiliary plane to project the plane shapes.
1.D - Performance Objectives:
At the end of this lecture the student should be able to:
 use the Auxiliary plane to project the plane shapes.
2. Pre test
U
The equilateral lamina ABC is placed perpendicular to the V.P and having the
following data:
A(8,2) B(14,11) left of A C(2,11) left of A
The distance of projector BC = 0
Required:
1. Draw scale 1:1 the elevation and plane of the lamina
2. Project a view on an auxiliary plane perpendicular to both the H.P and the V.P.
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Descriptive Geometry
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4. Quiz
The equilateral lamina ABC is placed perpendicular to the V.P and having the
following data:
A(2,2) B(2,10) left of A C(2,11) left of A
The distance of projector AB = 6 cm
Required:
1. Draw scale 1:1 the elevation and plane of the lamina.
2. Project a view on an auxiliary plane perpendicular to both the H.P and the V.P.
3. Find the coordinates of point C.
5. Post test
Writ the procedures to project the plane shapes on the Auxiliary plane.
6. References
- (Descriptive Geometry), Dr. Yousef Nicola , National library-Baghdad 1976
- (An analytical introduction to Descriptive Geometry), Adrian B. Biran, Oxford,
UK Samples - August 2005
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Descriptive Geometry
By: Ameer Tofan
Week Number: 25-26
Open cylinder and definition
1. Over view
1.A –Target population:
- For students of second class, Technical college-Baghdad, Engineering
Techniques of Materials, Welding, Dies and Tools, Automotive and
Refrigeration and air conditioning.
- For students of first class, Technical college-Baghdad, Engineering
Techniques of Surveying.
1.B – Rationale:
Open cylinder and definition, is very important subject to be studied in
order to project the shapes on the cylindrical surface.
1.C – Central Idea:
 Open the surface of cylinder.
1.D - Performance Objectives:
At the end of this lecture the student should be able to:
 project the shapes on the cylindrical surface.
2. Pre test
U
How can make a cylinder by surface of rectangle.
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Descriptive Geometry
3. The text
By: Ameer Tofan
***********102c
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232
Descriptive Geometry
By: Ameer Tofan
4. Quiz ***** 232
A right cylinder of height 9 cm and its base diameter 3 cm, The pyramid, is placed
with its axis perpendicular to the H.P.
Required:
1. draw scale 1:1 the elevation and plane of the pyramid.
2. on the elevation, draw the development of its surface.
5. Post test
What do you see with the open a cylinder.
6. References
- (Descriptive Geometry), Dr. Yousef Nicola , National library-Baghdad 1976
- (An analytical introduction to Descriptive Geometry), Adrian B. Biran, Oxford,
UK Samples - August 2005
Page
48
Descriptive Geometry
By: Ameer Tofan
Week Number: 27-28
Open cone and definition
1. Over view
1.A –Target population:
- For students of second class, Technical college-Baghdad, Engineering
Techniques of Materials, Welding, Dies and Tools, Automotive and
Refrigeration and air conditioning.
- For students of first class, Technical college-Baghdad, Engineering
Techniques of Surveying.
1.B – Rationale:
Open cylinder and definition, is very important subject to be studied in
order to project the shapes on the surface of cone.
1.C – Central Idea:
 Open the surface of cone.
1.D - Performance Objectives:
At the end of this lecture the student should be able to:
 project the shapes on the surface of cone.
2. Pre test
U
What do you see by open the surface of the cone?
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Descriptive Geometry
3. The text
By: Ameer Tofan
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135c
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4. Quiz *****225
A right pentagonal pyramid of height 10 cm and its base is a square of side 4 cm,
The pyramid is placed with its axis perpendicular to the H.P.
Required:
1. draw scale 1:1 the elevation and plane of the pyramid.
2. on the elevation, draw the development of its surface.
5. Post test
Why are we open the surface of cone.
6. References
- (Descriptive Geometry), Dr. Yousef Nicola , National library-Baghdad 1976
- (An analytical introduction to Descriptive Geometry), Adrian B. Biran, Oxford,
UK Samples - August 2005
Page
52
Descriptive Geometry
By: Ameer Tofan
Week Number: 29-30
Cut the cone using Auxiliary plane
1. Over view
1.A –Target population:
- For students of second class, Technical college-Baghdad, Engineering
Techniques of Materials, Welding, Dies and Tools, Automotive and
Refrigeration and air conditioning.
- For students of first class, Technical college-Baghdad, Engineering
Techniques of Surveying.
1.B – Rationale:
Cut the cone using Auxiliary plane, is very important subject to be studied
in order to draw the section of the cone.
1.C – Central Idea:
 draw the section of the cone by the Auxiliary plane .
1.D - Performance Objectives:
At the end of this lecture the student should be able to:
 draw the section of the cone by the Auxiliary plane.
2. Pre test
U
Draw the hyperbolic curve .
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4. Quiz
A right pentagonal pyramid of height 16 cm and base-side 8 cm, is placed with its
axis vertical. Its base ABCDE having A(2,2) and the side CD is parallel to the G.L,
The pyramid is cut by a plane P-P parallel the H.P and 10 cm above the H.P.
Required:
1. draw scale 1:1 the elevation.
2. sectional plane P-P.
5. Post test
What will see by cut the cone with the inclined auxiliary plane with its base?
a) hyperbolic b)circle c) rectangle
6. References
- (Descriptive Geometry), Dr. Yousef Nicola , National library-Baghdad 1976
- (An analytical introduction to Descriptive Geometry), Adrian B. Biran, Oxford,
UK Samples - August 2005
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