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What to expected in class
GEOMETRICAL DRAWING
• Go through your topics notes before you come to
your class
• NOTES
• Each one of you should post class notes
immediately after the google classroom
• CLASS RECORDINGS
• Do your assignments honestly and post on time
• WORKED OUT EXAMPLES
• Assignments at least 1 per each topic
• ASSIGNEMENTS
• EXAMINATIONS / TEST PAPERS
INTRODUCTION
1
• GOOGLE CLASSROOM
4
Architectural Learning
University Examinations
• What is Architecture
• 4 Hour Exam
• CORRECTNESS
• ANNOTATION
• How do you learn Designing
• DIMENSIONS
• NOTES
• 8 short note question (5 marks each)
•
•
•
•
• Information
• Knowledge
All compulsory
2 questions each from each module
8 x 5 = 40 marks
Expects sketches where necessary
• CLARITY
• LINE WEIGHT
• NEATNESS
• Wisdom
• 8 Drawings
• 2 each from each module. You have to answer one out of
these two
• 4 x 15 = 60 marks
2
5
SYLLABUS
Drawing requirement
2014 Syllabus
• Sample
Scale
Conics
Spirals
Helix
• MODULE 2
• Points & Lines
• Planes
• Solids
• MODULE 3
• Intersection of solids
• Sections of solids
• Development of surfaces
• MODULE 4
• Isometric drawing
• Perspective drawing
3
•
•
•
•
•
• CORRECTNESS
• Draw projections of line ‘AB’, where point ‘A’ is ‘da’ units
in front of Vertical Plane (VP) and ‘ha’ units above
Horizontal Plane (HP); while point ‘B’ is ‘db’ units in front
of Vertical Plane (VP) and ‘hb’ units above Horizontal
Plane.
• Question No : 1
• Note: in this case, ‘da’ = ‘db’
Triangles, quadrilaterals, trapezoids, regular polygons.
Tangent, curves.
Conic sections, spirals, helix,
Involutes, cycloids trochoids,
Plain scale, diagonal scale
b’
• MODULE 2
a’
• Projection of solids, sections of solid prisms, pyramids,
cylinders cones, spheres
• Development of surfaces of solids
• Intersection of surfaces
θ
• ANNOTATION
• DIMENSIONS
• NOTES
• CLARITY
• LINE WEIGHT
• NEATNESS
VP
ha
•
•
•
•
2021 Syllabus
• MODULE 1
• MODULE 3
x
• Isometric, axonometric and Oblique views
• Perspective, one-point, two-point, and 3 point
y
da (db)
• MODULE 1
• MODULE 4
• Sciography, Shadow of lines, planes, and simple solids
due to near and distant sources.
• Application of sciography on pictorial view
a
b
HP
projection of line
6
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Perpendicular
Bisector
Prerequisites – understanding basic geometric Constructions
• Line bisector
• Given a line segment AB ; Construct the line bisector.
A perpendicular bisector can be defined as a
line segment which intersects another line
perpendicularly and divides it into two equal
parts.
• Draw two arcs with
center A and B; and
with same radius bigger
than half the length of
AB
.
01
A
B
Basic geometric constructions
7
10
Prerequisites – understanding basic geometric Constructions
Prerequisites – understanding basic geometric Constructions
• Line bisector
• Line bisector
• Given a line segment AB ; Construct the line bisector.
A
• Given a line segment AB ; Construct the line bisector.
B
A
8
O
B
11
Prerequisites – understanding basic geometric Constructions
Prerequisites – understanding basic geometric Constructions
• Line bisector
• Line bisector
• Given a line segment AB ; Construct the line bisector.
• Given a line segment AB ; Construct the line bisector.
• Draw two arcs with
center A and B; and
with same radius bigger
than half the length of
AB
A
9
• Draw two arcs with
center A and B; and
with same radius bigger
than half the length of
AB
• Join the arc intersection
with a line
• The line intersect the
segment AB at O
B
A
O
90 o
B
• Draw two arcs with
center A and B; and
with same radius bigger
than half the length of
AB
• Join the arc intersection
with a line
• The line intersect the
segment AB at O
• The line insect 90th with
AB and hence it is a
perpendicular bisector
of AB
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Perpendicular to a
given line at a given
point on it
Prerequisites – understanding basic geometric Constructions
• Perpendicular to a Line
• Construct a perpendicular through a given point O on a line.
•
• Draw a circle with center O which
intersects the line at two points A
&B
02
A
B
• Draw two arcs with center A and
B; and with same radius bigger
than half the length of AB
Basic geometric constructions
13
16
Prerequisites – understanding basic geometric Constructions
Prerequisites – understanding basic geometric Constructions
• Perpendicular to a Line
• Perpendicular to a Line
• Construct a perpendicular through a given point O on a line.
• Construct a perpendicular through a given point O on a line.
• Draw a circle with center O which
intersects the line at two points A
&B
O
A
14
B
• Draw two arcs with center A and
B; and with same radius bigger
than half the length of AB
17
Prerequisites – understanding basic geometric Constructions
Prerequisites – understanding basic geometric Constructions
• Perpendicular to a Line
• Perpendicular to a Line
• Construct a perpendicular through a given point O on a line.
• Construct a perpendicular through a given point O on a line.
• Draw a circle with center O which
intersects the line at two points A
&B
A
O
• Draw a circle with center O which
intersects the line at two points A
&B
B
A
O
90 o
B
• Draw two arcs with center A and
B; and with same radius bigger
than half the length of AB
• Join the arc intersection with a
line which will passing through the
point O and will be perpendicular
to Line AB
15
18
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Perpendicular to a
given line from a
given point outside
of it
Prerequisites – understanding basic geometric Constructions
• Perpendicular to a Line
• Construct a perpendicular to a line and passing through a given point O outside
of the line.
• Draw a circle with center O which
intersects the line at two points A
&B
O
03
A
B
• Draw two arcs with center A and
B; and with same radius bigger
than half the length of AB
Basic geometric constructions
19
22
Prerequisites – understanding basic geometric Constructions
Prerequisites – understanding basic geometric Constructions
• Perpendicular to a Line
• Perpendicular to a Line
• Construct a perpendicular to a line and passing through a given point O outside
of the line.
• Construct a perpendicular to a line and passing through a given point O outside
of the line.
• Draw a circle with center O which
intersects the line at two points A
&B
O
O
A
20
B
• Draw two arcs with center A and
B; and with same radius bigger
than half the length of AB
23
Prerequisites – understanding basic geometric Constructions
Prerequisites – understanding basic geometric Constructions
• Perpendicular to a Line
• Perpendicular to a Line
• Construct a perpendicular to a line and passing through a given point O outside
of the line.
• Construct a perpendicular to a line and passing through a given point O outside
of the line.
• Draw a circle with center O which
intersects the line at two points A
&B
• Draw a circle with center O which
intersects the line at two points A
&B
O
A
O
B
A
90 o
B
• Draw two arcs with center A and
B; and with same radius bigger
than half the length of AB
• Join the arc intersection with a
line which will passing through the
point O and will be perpendicular
to Line AB
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Angle bisector
Prerequisites – understanding basic geometric Constructions
• Angle bisector
• Given a two lines creating and angle θ ; Construct the line bisecting the angle θ.
A
• Draw a circle with center O and
intersects the lines OA & OB at C
& D respectively
C
E
θ/2
θ/2
04
• Draw two arcs with center C and
D; and with same radius and
intersects at point E
θ
O
B
D
Basic geometric constructions
25
28
Prerequisites – understanding basic geometric Constructions
Prerequisites – understanding basic geometric Constructions
• Angle bisector
• Angle bisector
• Given a two lines creating and angle θ ; Construct the line bisecting the angle θ.
• Given a two lines creating and angle θ ; Construct the line bisecting the angle θ.
A
A
• Draw a circle with center O and
intersects the lines OA & OB at C
& D respectively
C
E
• Draw two arcs with center C and
D; and with same radius and
intersects at point E
θ
O
O
B
26
B
D
• Draw the line connecting O and E
which will be bisecting the angle θ
29
Prerequisites – understanding basic geometric Constructions
Prerequisites – understanding basic geometric Constructions
• Angle bisector
• Angle bisector
• Given a two lines creating and angle θ ; Construct the line bisecting the angle θ.
• Given a two lines creating and angle θ ; Construct the line bisecting the angle θ.
A
A
• Draw a circle with center O and
intersects the lines OA & OB at C
& D respectively
C
C
θ/2
θ
O
27
E
θ/2
D
O
B
D
B
30
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60o & 30o angle
Prerequisites – understanding basic geometric Constructions
• 60 0 Angle
• Construct a line 60 0 with a given line
• Draw a circle with center O and
with any radius “r” intersecting
the lines OB at D
C
30o
30o
• Draw an arc with center D and
with same radius “r” and
intersecting circle at C
05
O
B
D
Basic geometric constructions
31
34
Prerequisites – understanding basic geometric Constructions
Prerequisites – understanding basic geometric Constructions
• 60 0 Angle
• 60 0 Angle
• Construct a line 60 0 with a given line
• Construct a line 60 0 with a given line
A
• Draw a circle with center O and
with any radius “r” intersecting
the lines OB at D
C
• Draw line OA passing through the
points O and C
60o
O
O
B
32
• <AOB = 600
B
D
35
Prerequisites – understanding basic geometric Constructions
Prerequisites – understanding basic geometric Constructions
• 60 0 Angle
• 30 0 Angle
• Construct a line 60 0 with a given line
• Construct a line 30 0 with a given line
A
• Draw a circle with center O and
with any radius “r” intersecting
the lines OB at D
• Draw a circle with center O and
with any radius “r” intersecting
the lines OB at D
C
E
• Draw line OA passing through the
points O and C
60o
O
33
D
O
B
• ∠ AOB = 600
D
B
• Furthermore, to create 30o angle,
create two more circles of same
radius with centers C and D
intersecting at point E
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Prerequisites – understanding basic geometric Constructions
Prerequisites – understanding basic geometric Constructions
• 30 0 Angle
• 45 0 Angle
• Construct a line 30 0 with a given line
• Construct a line 45 0 with a given line
A
• Draw a circle with center O and
with any radius “r” intersecting
the lines OB at D
C
E
• Draw line OA passing through the
points O and C
30o
O
A
• ∠ AOB = 600
30o
B
D
B
• Furthermore, to create 30o angle,
create two more circles of same
radius with centers C and D
intersecting at point E
• Line OE will bisect ∠ A0B
37
40
Prerequisites – understanding basic geometric Constructions
Prerequisites – understanding basic geometric Constructions
• Equilateral triangle
• 45 0 Angle
• Construct a line 30 0 with a given line
• Construct a line 45 0 with a given line
A
• Joining O, C and B will form an
equilateral triangle.
C
• Draw a perpendicular to AB
passing through a point O
E
A
O
D
O
90 o
B
B
38
41
45o angle
Prerequisites – understanding basic geometric Constructions
• 45 0 Angle
• Construct a line 45 0 with a given line
45o
• Draw a perpendicular to AB
passing through a point O
C
06
A
O
90 o
• Draw an arc with radius OA and
intersecting the perpendicular line
at C
B
Basic geometric constructions
39
42
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Prerequisites – understanding basic geometric Constructions
Prerequisites – understanding basic geometric Constructions
• 45 0 Angle
• Congruent Angles
• Construct a line 45 0 with a given line
• Draw a perpendicular to AB
passing through a point O
C
A
45o
• Draw an arc with center A intersecting the lines AB
and AC at D and E respectively
• Match the given angle
C
• Draw an arc with radius OA and
intersecting the perpendicular line
at C
90 o
B
O
• The line AC will create an angle of
45o with AB
P
E
A
θ
B
D
Q
43
46
Congruent Angles
Prerequisites – understanding basic geometric Constructions
• Congruent Angles
θ
• Draw an arc with center A intersecting the lines AB
and AC at D and E respectively
• Draw another angle with same radius with P as
center intersecting the line PQ at S
• Match the given angle
Congruent angles are angles with exactly same
measure.
C
07
P
E
A
θ
B
S
D
Q
Basic geometric constructions
44
47
Prerequisites – understanding basic geometric Constructions
Prerequisites – understanding basic geometric Constructions
• Congruent Angles
• Congruent Angles
• Match the given angle
• Draw an arc with center A intersecting the lines AB
and AC at D and E respectively
• Draw another arc with same radius with P as center
intersecting the line PQ at S
• Draw an arc with center S and radius DE intersect
the arc at T
• Match the given angle
C
C
P
A
θ
P
E
A
B
θ
B
D
Q
45
T
S
Q
48
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Prerequisites – understanding basic geometric Constructions
Prerequisites – understanding basic geometric Constructions
• Congruent Angles
• Points and Lines
• Match the given angle
C
E
• Draw an arc with center A intersecting the lines AB
and AC at D and E respectively
• Draw another arc with same radius with P as center
intersecting the line PQ at S
• Draw an arc with center S and radius DE intersect
the arc at T
• Connect the points P and T to construct the
matching angle θ
P
T
• Line parallel to a given line through a given point
• Draw a line passing through the given
point P and intersect the given line (at
A) at any angle
P
θ
A
θ
B
S
D
Q
49
B
52
Line Parallel to a
given line
Prerequisites – understanding basic geometric Constructions
• Points and Lines
• Line parallel to a given line through a given point
• Draw a line passing through the given
point P and intersect the given line (at
A) at any angle
• Draw an arc with A as center and with
any radius (r) , and intersecting the lines
at points B and C
P
08
B
A
C
Basic geometric constructions
50
53
Prerequisites – understanding basic geometric Constructions
Prerequisites – understanding basic geometric Constructions
• Points and Lines
• Points and Lines
• Line parallel to a given line through a given point
• Line parallel to a given line through a given point
Q
P
P
• Draw a line passing through the given
point P and intersect the given line (at
A) at any angle
• Draw an arc with A as center and with
any radius (r) , and intersecting the lines
at points B and C
• Draw a circle with the same radius r
and with center point P, intersecting the
line at Q as indicated in the figure.
B
C
A
B
51
54
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Prerequisites – understanding basic geometric Constructions
Prerequisites – understanding basic geometric Constructions
• Points and Lines
• Points and Lines
• Line parallel to a given line through a given point
Q
R
P
B
C
• Draw a line passing through the given
point P and intersect the given line (at
A) at any angle
• Draw an arc with A as center and with
any radius (r) , and intersecting the lines
at points B and C
• Draw a circle with the same radius r
and with center point P, intersecting the
line at Q as indicated in the figure.
• Draw and arc with Q as center and with
a radius equal to BC, intersecting the
circle at R
• In fact, we created vertices of two
congruent triangles PQR and ABC
• Dividing a given line into N equal parts
A
How to divide a given line AB into 7 equal
parts
B
A
55
58
Prerequisites – understanding basic geometric Constructions
Prerequisites – understanding basic geometric Constructions
• Points and Lines
• Points and Lines
• Draw a line passing through the given
point P and intersect the given line (at
• Line parallel to a given line through a given point A) at any angle
• Draw an arc with A as center and with
any radius (r) , and intersecting the lines
at points B and C
Q
• Draw a circle with the same radius r
and with center point P, intersecting the
line at Q as indicated in the figure.
R
P
• Draw and arc with Q as center and with
a radius equal to BC, intersecting the
circle at R
B
• In fact, we created vertices of two
congruent triangles PQR and ABC
• Join the points P and R, the line PR is
A
parallel to the given line.
C
56
• Dividing a given line into N equal parts
A
How to divide a given line AB into 7 equal
parts
• Draw a line passing through A and at any
angle . Mark an arc with any radius (r) on the
line with center A.
B
59
Dividing a line segment
into equal parts
Prerequisites – understanding basic geometric Constructions
• Points and Lines
• Dividing a given line into N equal parts
Basic Proportionality theorem by Thales
Any two equiangular triangles, the ratio of any two
corresponding sides is always the same. If two triangles are
similar to each other then,
i) Corresponding angles of both the triangles are equal
ii) Corresponding sides of both the triangles are in
proportion to each other
A
09
How to divide a given line AB into 7 equal
parts
• Draw a line passing through A and at any
angle . Mark an arc with any radius (r) on the
line with center A.
• Mark six more arcs with same radius ( r) on
the line as indicated. (7 equal division of ‘r’
units each)
B
Basic geometric constructions
57
60
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Prerequisites – understanding basic geometric Constructions
Prerequisites – understanding basic geometric Constructions
• Points and Lines
• Points and Lines
• Dividing a given line into N equal parts
C
A
B
How to divide a given line AB into 7 equal
parts
• Draw a line passing through A and at any
angle . Mark an arc with any radius (r) on the
line with center A.
• Mark six more arcs with same radius ( r) on
the line as indicated. (7 equal division of ‘r’
units each)
• Connect the intersection of last arc and line
with the point B forming line BC as
indicated
• Dividing a given line into N equal parts
C
A
B
D
61
How to divide a given line AB into 7 equal
parts
• Draw a line passing through A and at any
angle . Mark an arc with any radius (r) on the
line with center A.
• Mark six more arcs with same radius ( r) on
the line as indicated. (7 equal division of ‘r’
units each)
• Connect the intersection of last arc and line
with the point B forming line BC as
indicated
• Draw two arcs with radius BC and AC and
with A and B respectively.
• Let D be the intersecting point of the arcs.
Connect D with A and B.
• [AC=BD & BC=AD]
• Divide the line BD into 7 equal parts
marking arc of ‘r’ unit radius as indicated.
64
Prerequisites – understanding basic geometric Constructions
Prerequisites – understanding basic geometric Constructions
• Points and Lines
• Points and Lines
• Dividing a given line into N equal parts
C
A
B
How to divide a given line AB into 7 equal
parts
• Draw a line passing through A and at any
angle . Mark an arc with any radius (r) on the
line with center A.
• Mark six more arcs with same radius ( r) on
the line as indicated. (7 equal division of ‘r’
units each)
• Connect the intersection of last arc and line
with the point B forming line BC as
indicated
• Draw two arcs with radius BC and AC and
with A and B respectively.
• Dividing a given line into N equal parts
C
A
B
D
62
How to divide a given line AB into 7 equal
parts
• Draw a line passing through A and at any
angle . Mark an arc with any radius (r) on the
line with center A.
• Mark six more arcs with same radius ( r) on
the line as indicated. (7 equal division of ‘r’
units each)
• Connect the intersection of last arc and line
with the point B forming line BC as
indicated
• Draw two arcs with radius BC and AC and
with A and B respectively.
• Let D be the intersecting point of the arcs.
Connect D with A and B.
• [AC=BD & BC=AD]
• Divide the line BD into 7 equal parts
marking arc of ‘r’ unit radius as indicated.
• Connect the intersection points of arc and
lines as indicated
65
Prerequisites – understanding basic geometric Constructions
Prerequisites – understanding basic geometric Constructions
• Points and Lines
• Points and Lines
• Dividing a given line into N equal parts
C
A
B
How to divide a given line AB into 7 equal
parts
• Draw a line passing through A and at any
angle . Mark an arc with any radius (r) on the
line with center A.
• Mark six more arcs with same radius ( r) on
the line as indicated. (7 equal division of ‘r’
units each)
• Connect the intersection of last arc and line
with the point B forming line BC as
indicated
• Draw two arcs with radius BC and AC and
with A and B respectively.
• Let D be the intersecting point of the arcs.
Connect D with A and B.
• [AC==BD & BC==AD]
• Dividing a given line into N equal parts
C
A
D
D
63
66
B
How to divide a given line AB into 7 equal
parts
• Draw a line passing through A and at any
angle . Mark an arc with any radius (r) on the
line with center A.
• Mark six more arcs with same radius ( r) on
the line as indicated. (7 equal division of ‘r’
units each)
• Connect the intersection of last arc and line
with the point B forming line BC as
indicated
• Draw two arcs with radius BC and AC and
with A and B respectively.
• Let D be the intersecting point of the arcs.
Connect D with A and B.
• [AC=BD & BC=AD]
• Divide the line BD into 7 equal parts
marking arc of ‘r’ unit radius as indicated.
• Connect the intersection points of arc and
lines as indicated
• Essentially Line AB gets divided into 7
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Centre of a Circle
Prerequisites – understanding basic geometric Constructions
• Circle
• Finding the Center of a given circle
• Draw a chord AB connecting any two points
B
• Construct a perpendicular bisector of chord AB
intersecting the circle at C and D
C
10
A
D
Basic geometric constructions
67
70
Prerequisites – understanding basic geometric Constructions
Prerequisites – understanding basic geometric Constructions
• Circle
• Circle
• Finding the Center of a given circle
• Finding the Center of a given circle
• Draw a chord AB connecting any two points
B
• Construct a perpendicular bisector of chord AB
intersecting the circle at C and D (Diameter)
C
• Construct a perpendicular bisector of CD with
midpoint O
A
O
D
68
71
Prerequisites – understanding basic geometric Constructions
Tangents to a Circle
• Circle
• Finding the Center of a given circle
The tangent to a circle is a straight line which
touches the circle at a single point. The point
where the tangent touches a circle is known as
the point of tangency or the point of contact.
• Draw a chord AB connecting any two points
B
11
A
Basic geometric constructions
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72
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Prerequisites – understanding basic geometric Constructions
Prerequisites – understanding basic geometric Constructions
• Circle
• Circle
• Constructing tangents to a circle from a given point
• Constructing tangents to a circle from a given point
• Draw a line connecting O and P
• Let O be the center of the circle and P be the given
point
• Construct a perpendicular bisection
of line OP
T1
• Mark the midpoint M
O
O
P
M
P
• Draw an arch with Center M and
radius OM
• March the intersecting points of the
arc with the circle as T1 and T2
T2
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76
Prerequisites – understanding basic geometric Constructions
Prerequisites – understanding basic geometric Constructions
• Circle
• Circle
• Constructing tangents to a circle from a given point
• Constructing tangents to a circle from a given point
• Draw a line connecting O and P
• Let O be the center of the circle and P be the given
point
• Draw a line connecting O and P
• Construct a perpendicular bisection
of line OP
T1
• Mark the midpoint M
O
P
O
M
P
• Draw an arch with Center M and
radius OM
• March the intersecting points of the
arc with the circle as T1 and T2
T2
74
• Lines connecting Point P with T1 and
T2 are tangent to the circle.
77
Prerequisites – understanding basic geometric Constructions
Inscribed Circles of
Triangles
• Circle
• Constructing tangents to a circle from a given point
Given a triangle, an inscribed circle is the
largest circle contained within the triangle. The
inscribed circle will touch each of the three
sides of the triangle in exactly one point. The
center of the circle inscribed in a triangle is the
incenter of the triangle, the point where the
angle bisectors of the triangle meet.
• Draw a line connecting O and P
• Construct a perpendicular bisection of
line OP
• Mark the midpoint M
O
M
12
P
Basic geometric constructions
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Prerequisites – understanding basic geometric Constructions
Prerequisites – understanding basic geometric Constructions
• Circle
• Circle
A
• Circle inscribed in a given triangle
A
• Circle inscribed in a given triangle
C
C
• Construct angle bisectors of ∠ A and ∠B
• Mark the intersection of the bisectors as O
• Draw a line perpendicular to AC passing
through point O
O
B
B
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82
Prerequisites – understanding basic geometric Constructions
Prerequisites – understanding basic geometric Constructions
• Circle
• Circle
A
• Circle inscribed in a given triangle
A
• Circle inscribed in a given triangle
C
• Construct angle bisectors of ∠ A and ∠B
C
• Construct angle bisectors of ∠ A and ∠B
• Mark the intersection of the bisectors as O
• Draw a line perpendicular to AC passing
through point O
O
B
B
80
83
Prerequisites – understanding basic geometric Constructions
Prerequisites – understanding basic geometric Constructions
• Circle
• Circle
A
• Circle inscribed in a given triangle
A
• Circle inscribed in a given triangle
C
• Construct angle bisectors of ∠ A and ∠B
P
C
• Construct angle bisectors of ∠ A and ∠B
• Mark the intersection of the bisectors as O
• Mark the intersection of the bisectors as O
• Draw a line perpendicular to AC passing
through point O
O
O
• Mark the intersecting point of the
perpendicular and Line AC as P
B
81
B
84
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17-11-2022
Prerequisites – understanding basic geometric Constructions
• Circle
Prerequisites – understanding basic geometric Constructions
• Circle
A
• Circle inscribed in a given triangle
• Circle circumscribed on a given triangle
P
C
• Construct angle bisectors of ∠ A and ∠B
• Construct perpendicular bisectors line AB
A
• Mark the intersection of the bisectors as O
C
• Draw a line perpendicular to AC passing
through point O
O
• Mark the intersecting point of the
perpendicular and Line AC as P
• Construct the inscribed circle with center O
and radius OP
B
B
85
88
Circumscribed
Circles of Triangles
Prerequisites – understanding basic geometric Constructions
• Circle
• Circle circumscribed on a given triangle
Given a triangle, the circumscribed circle is the
circle that passes through all three vertices of
the triangle. The center of the circumscribed
circle is the circumcenter of the triangle, the
point where the perpendicular bisectors of the
sides meet.
• Construct perpendicular bisectors line AB
• Construct perpendicular bisectors line BC
A
C
• Mark intersecting point of the perpendicular
lines as O
O
13
B
Basic geometric constructions
86
89
Prerequisites – understanding basic geometric Constructions
Prerequisites – understanding basic geometric Constructions
• Circle
• Circle
• Circle circumscribed on a given triangle
• Circle circumscribed on a given triangle
A
• Construct perpendicular bisectors line AB
• Construct perpendicular bisectors line BC
C
• Mark intersecting point of the perpendicular
lines as O
A
C
O
• Draw the circle with center O and radius
OA. The circle will be passing through other
vertices ( B and C ) of the triangle as well
B
87
B
90
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17-11-2022
Regular pentagon
inscribed in a circle
Prerequisites – understanding basic geometric Constructions
• Pentagon
• Inscribe a regular pentagon in a given circle with center O
A
14
• Draw the perpendicular bisector
of AF passing through O and mark
the point G intersecting the circle.
O
G
Basic geometric constructions
91
• Draw a line passing through the
center and mark intersecting point
A and F
F
94
Prerequisites – understanding basic geometric Constructions
Prerequisites – understanding basic geometric Constructions
• Pentagon
• Pentagon
• Inscribe a regular pentagon in a given circle with center O
• Inscribe a pentagon in a given circle with center O
A
O
• Draw a line passing through the
center and mark intersecting point
A and F
• Draw the perpendicular bisector
of AF passing through O and mark
the point G intersecting the circle.
O
H
G
• Draw the perpendicular bisector
of OG and mark midpoint H.
F
92
95
Prerequisites – understanding basic geometric Constructions
Prerequisites – understanding basic geometric Constructions
• Pentagon
• Pentagon
• Inscribe a pentagon in a given circle with center O
A
• Inscribe a regular pentagon in a given circle with center O
• Draw a line passing through the
center and mark intersecting point
A and F
A
O
• Draw a line passing through the
center and mark intersecting point
A and F
• Draw the perpendicular bisector
of AF passing through O and mark
the point G intersecting the circle.
O
H
F
93
G
• Draw the perpendicular bisector
of OG and mark midpoint H. Draw
a circle with H as center and HO
as radius
F
96
16
17-11-2022
Prerequisites – understanding basic geometric Constructions
Prerequisites – understanding basic geometric Constructions
• Pentagon
• Pentagon
• Inscribe a regular pentagon in a given circle with center O
A
• Draw
O a line connecting F and H.
• Inscribe a regular pentagon in a given circle with center
• Draw a line passing through the
center and mark intersecting point
A and F
• Draw the perpendicular bisector
of AF passing through O and mark
the point G intersecting the circle.
J
O
H
G
• Construct an arc with center F
and radius FJ intersecting the
given circle at B and E.
E
J
• Draw the perpendicular bisector
of OG and mark midpoint H. Draw
a circle with H as center and HO
as radius
97
B
O
H
• Draw a line connecting F and H.
Extend the line to intersect the
circle (with center H) at J
F
Extend the line to intersect the
circle (with center H) at J
A
G
• Construct an arc with center E
and radius EA intersecting the
given circle at D
D
F
100
Prerequisites – understanding basic geometric Constructions
Prerequisites – understanding basic geometric Constructions
• Pentagon
• Pentagon
• Draw
O a line connecting F and H.
• Inscribe a regular pentagon in a given circle with center
Extend the line to intersect the
circle (with center H) at J
A
• Draw
O a line connecting F and H.
• Inscribe a regular pentagon in a given circle with center
• Construct an arc with center F
and radius FJ intersecting the
given circle at B and E.
E
J
Extend the line to intersect the
circle (with center H) at J
A
• Construct an arc with center F
and radius FJ intersecting the
given circle at B and E.
E
B
J
O
B
O
H
H
G
G
• Construct an arc with center E
and radius EA intersecting the
given circle at D
• Construct an arc with center B
and radius BA intersecting the
given circle at C
D
F
C
F
98
101
Prerequisites – understanding basic geometric Constructions
Prerequisites – understanding basic geometric Constructions
• Pentagon
• Pentagon
• Draw
O a line connecting F and H.
• Inscribe a regular pentagon in a given circle with center
Extend the line to intersect the
circle (with center H) at J
A
• Draw
O a line connecting F and H.
• Inscribe a regular pentagon in a given circle with center
• Construct an arc with center F
and radius FJ intersecting the
given circle at B and E.
E
J
Extend the line to intersect the
circle (with center H) at J
A
• Construct an arc with center F
and radius FJ intersecting the
given circle at B and E.
E
B
J
O
B
O
H
H
G
G
• Construct an arc with center E
and radius EA intersecting the
given circle at D
• Construct an arc with center B
and radius BA intersecting the
given circle at C
D
F
99
C
F
• Join points ABCDE to form the
regular pentagon
102
17
17-11-2022
Prerequisites – understanding basic geometric Constructions
• Pentagon
• Inscribe a regular pentagon in a given circle with center O
A
E
J
B
O
H
D
G
C
F
103
George Jacob P
104
18