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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

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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

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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

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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

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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

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

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

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A portion of the circumference of a circle (Fig. 2.11).

2.7 Arcs

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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

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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

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Fig. 2.13: A tangent to an arc

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The End

KEJ3103 Drawing Engineering

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