Ch2 Geometric

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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.

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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.

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    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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    Fig. 2.3: The alphabet of lines

    2.2 Geometric elements: Straight Lines

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    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

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    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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    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

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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

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