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KEJ3103
DRAWING ENGINEERING
KEJ3103 Drawing Engineering
Chapter 2
GEOMETRIC CONSTRUCTION
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2.1 Introduction
The solution of many graphical problems requires the use
__________ and geometric construction.
Geometry provides the __________ for the engineering
design process.
Engineering geometry is the basic geometric elements and
forms used in engineering design.
KEJ3103 Drawing Engineering
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2.1 Introduction
The study of geometry can be broken into two broad types
(Fig. 2.1):1.________ geometry: two dimensions;
2. ________ geometry: three dimensions.
KEJ3103 Drawing Engineering
Fig. 2.1: Types of geometry
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A straight line is the shortest distance between any two
points (Fig. 2.2).
2.2 Geometric elements: Straight Lines
KEJ3103 Drawing Engineering
Fig. 2.2: Types of straight line
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KEJ3103 Drawing Engineering
Fig. 2.3: The alphabet of lines
2.2 Geometric elements: Straight Lines
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KEJ3103 Drawing Engineering
Fig. 2.4: The variations of lines
2.2 Geometric elements: Straight Lines
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A fundamental application of geometric construction involves
drawing lines at specified angels to each other. Fig. 2.5 gives names and definitions of various angles.
2.3 Geometric elements: Angels
KEJ3103 Drawing Engineering
Acute angel
< 90
Right angel
Exactly 90
Obtuse angel
Between 90 and 180
Straight angel
Exactly 180
Reflex angel
Between 180 and 360
Fig. 2.5:
Standards angels
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2.3.1 Angels construction
1. Copying an angle.
2. Constructing a 30 angle.
3. Constructing a 45 angle.
4. Constructing a 60 angle.
5. Constructing a 90 angle (perpendicular, right angle) at:
5.1 The end of a line segment.
5.2 A point on a line segment.
5.3 Through a point not on a line segment.
5.4 The midpoint of a line segment.
2.3 Geometric elements: Angels
KEJ3103 Drawing Engineering
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Is a _________ plane figure of any number of sides.
If the sides of a polygon are equal in length, the polygon is a_______ polygon.
A regular polygon can be inscribed in a circle and all its corner
points will lie on the circle (Fig. 2.6).
The sum of the angles inside any polygon is S = (n-2) x 180,where n is the number of sides of the polygon.
2.4 Geometric elements: Polygons
KEJ3103 Drawing Engineering
Fig. 2.6:
Example of regular polygon:Pentagon (5 sides)
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2.4.1 Triangles
A 3 sided polygon (Fig.2.7). The sum of the interior angels of a triangle is _______ 180.
2.4 Geometric elements: Polygons
KEJ3103 Drawing EngineeringFig. 2.7: Types of triangles and their definitions
Isosceles
2 sides equal
Equilateral
All sides
equal
Scalene
No sides
equal
Right triangle
One angle 90
Obtuse
One angle greater
than 90
Acute
All angles less
than 90
Equiangular
All interior angles equal
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2.4.1 Triangles
Constructing a triangles, please see attachments:1. 30-60-90 triangle.
2. Isosceles triangle given the base and one side.
2.4 Geometric elements: Polygons
KEJ3103 Drawing Engineering
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2.4.2 Quadrilateral
Is a 4 sided polygon of any shape (Fig.2.8) . The sum of the interior angels of a triangle is ______.
2.4 Geometric elements: Polygons
KEJ3103 Drawing EngineeringFig. 2.8: Types of quadrilaterals and their definitions
Square
All sides equal, all
angles 90
Rectangle
Opposite sides
equal, all angles
90
Parallelogram
Opposite sides
parallel
Trapezoid
Two sides parallel Rhombus
Opposite sides
parallel and equal
Kite
Adjacent pairs of
sides equal
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2.4.3 Circle
A line forming a __________, every point on which is a fixeddistance from a center point (Fig.2.9).
A circle is constructed by swinging a radius from a fixed point
through 360.
The sum of the interior angels of a triangle is always 180.
2.4 Geometric elements: Polygons
KEJ3103 Drawing EngineeringFig. 2.9: Elements of a circle and their definitions
Diameter
Radius
Tangent
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2.5 Geometric solids
KEJ3103 Drawing EngineeringFig. 2.10: Types of geometric solids
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2.6.1 Lines
Perpendicular bisector of a line segment.2.6.2 Angels
Bisect an angel.
2.6 Bisecting lines and angels
KEJ3103 Drawing Engineering
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A portion of the circumference of a circle (Fig. 2.11).
2.7 Arcs
KEJ3103 Drawing Engineering
Fig. 2.11: An arc
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Lines are parallel if they lie in the same plane, and are the
same distance apart over their entire length (Fig. 2.12).
2.8 Parallel lines
KEJ3103 Drawing Engineering
Fig. 2.12: A parallel line
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A line that contacts an arc or circle at only one point
(Fig.2.13).
2.9 Tangents
KEJ3103 Drawing Engineering
Fig. 2.13: A tangent to an arc
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The End
KEJ3103 Drawing Engineering