# Polygons. Hidden Lines Practices.

```GEOMETRIC
CONSTRUCTION
CHAPTERFOUR
OBJECTIVES
1. Identify the geometry that makes up basic 2D drawings.
2. Use board drafting or 2D CAD skills to create technical
figures.
drawing with manual instruments
Technical Drawing with Engineering Graphics, 14/e
Giesecke, Hill, Spencer, Dygdon, Novak, Lockhart, Goodman
2
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GEOMETRY REVIEW
• Triangles
• Polygons
• Circles
• Arcs
Technical Drawing with Engineering Graphics, 14/e
Giesecke, Hill, Spencer, Dygdon, Novak, Lockhart, Goodman
3
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BISECTING A LINE OR
CIRCULAR ARC
Compass system
Triangle and T-Square System
Technical Drawing with Engineering Graphics, 14/e
Giesecke, Hill, Spencer, Dygdon, Novak, Lockhart, Goodman
4
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BISECTING A LINE WITH TRIANGLE
AND T-SQUARE
From endpoints A and B, draw construction lines at 30&deg;, 45&deg;, or 60&deg; with the given line.
Then, through their intersection, C, draw a line perpendicular to the given line to locate
the center D…
Technical Drawing with Engineering Graphics, 14/e
Giesecke, Hill, Spencer, Dygdon, Novak, Lockhart, Goodman
5
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Triangles
Inclined lines can be drawn at standard angles with the 45&deg; triangle and the
30&deg; x 60&deg; triangle. The triangles are transparent so that you can see the lines
of the drawing through them. A useful combination of triangles is the 30&deg; x 60&deg;
triangle with a long side of 10&quot; and a 45&deg; triangle with each side 8&quot; long.
Technical Drawing with Engineering Graphics, 14/e
Giesecke, Hill, Spencer, Dygdon, Novak, Lockhart, Goodman
6
&copy; 2012, 2009, 2003, Pearson Higher Education,
Any Angle in 15&deg; Increments
With only a 30&deg; x 60&deg;
triangle and a 45&deg;
triangle, you can draw
any angle in 15&deg;
increments
The bottom
of the triangle in
each case is resting
T-square. Twenty-four 15&deg;
sectors are possible with just
these two triangles used
singly or in combination.
Technical Drawing with Engineering Graphics, 14/e
Giesecke, Hill, Spencer, Dygdon, Novak, Lockhart, Goodman
7
&copy; 2012, 2009, 2003, Pearson Higher Education,
Protractors
For measuring or setting off angles other than those obtainable with
triangles, use a protractor.
Plastic protractors are
satisfactory for most
angular measurements
Nickel silver protractors are
available when high accuracy
is required
Technical Drawing with Engineering Graphics, 14/e
Giesecke, Hill, Spencer, Dygdon, Novak, Lockhart, Goodman
8
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ANGLES…
BISECTING AN ANGLE
TRANSFERRING AN
ANGLE
Technical Drawing with Engineering Graphics, 14/e
Giesecke, Hill, Spencer, Dygdon, Novak, Lockhart, Goodman
9
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TRIANGLES…
DRAWING A TRIANGLE
WITH SIDES GIVEN
DRAWING A RIGHT
TRIANGLE WITH
HYPOTENUSE AND ONE
SIDE GIVEN
Technical Drawing with Engineering Graphics, 14/e
Giesecke, Hill, Spencer, Dygdon, Novak, Lockhart, Goodman
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DRAWING AN EQUILATERAL
TRIANGLE
Alternative Method
Technical Drawing with Engineering Graphics, 14/e
Giesecke, Hill, Spencer, Dygdon, Novak, Lockhart, Goodman
11
&copy; 2012, 2009, 2003, Pearson Higher Education,
DRAWING A SQUARE
• T-square Method
• Diameters Method
• Inscribed Circle Method
You can use the AutoCAD Polygon
command to draw squares. The
Rectangle command is another quick
way to make a square in AutoCAD.
Technical Drawing with Engineering Graphics, 14/e
Giesecke, Hill, Spencer, Dygdon, Novak, Lockhart, Goodman
12
&copy; 2012, 2009, 2003, Pearson Higher Education,
DRAWING A REGULAR PENTAGON
Dividers Method
Technical Drawing with Engineering Graphics, 14/e
Giesecke, Hill, Spencer, Dygdon, Novak, Lockhart, Goodman
Geometric Method
13
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DRAWING A HEXAGON
Each side of a hexagon is equal to the radius of the circumscribed circle
Use a compass
Centerline Variation
Steps
Technical Drawing with Engineering Graphics, 14/e
Giesecke, Hill, Spencer, Dygdon, Novak, Lockhart, Goodman
14
&copy; 2012, 2009, 2003, Pearson Higher Education,
Drawing an Octagon
Given an inscribed circle, or distance
“across flats”, use a T-square or
straightedge and a 45&deg; triangle to draw
the eight sides tangent to the circle.
Technical Drawing with Engineering Graphics, 14/e
Giesecke, Hill, Spencer, Dygdon, Novak, Lockhart, Goodman
Given a circumscribed square, (the distance
“across flats”) draw the diagonals of the
square. Then, use the corners of the square
as centers and half the diagonal as the
radius to draw arcs cutting the sides
15
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DRAWING AN ARC TANGENT TO TWO
LINES AT RIGHT ANGLES
For small radii, such as 1/8R for fillets and rounds, it is not practicable
to draw complete tangency constructions. Instead, draw a 45&deg; bisector
of the angle and locate the center of the arc by trial along this line
Technical Drawing with Engineering Graphics, 14/e
Giesecke, Hill, Spencer, Dygdon, Novak, Lockhart, Goodman
16
&copy; 2012, 2009, 2003, Pearson Higher Education,
Technical Drawing with Engineering Graphics, 14/e
Giesecke, Hill, Spencer, Dygdon, Novak, Lockhart, Goodman
17
&copy; 2012, 2009, 2003, Pearson Higher Education,
!!!
Learn how to construct shown above shapes using ruler,
triangle and compass. Midterm Exam question.
Technical Drawing with Engineering Graphics, 14/e
Giesecke, Hill, Spencer, Dygdon, Novak, Lockhart, Goodman
18
&copy; 2012, 2009, 2003, Pearson Higher Education,