geometric construction
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Geometric Construction. Unit C. BY: K. L. TATRO CENTRAL HIGH SCHOOL EAST. Points and Lines. A Point represents a location in space or in a drawing and has no width, height, or depth. - PowerPoint PPT PresentationTRANSCRIPT
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Geometric Construction
Unit C
BY: K. L. TATRO CENTRAL HIGH SCHOOL EAST
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Points and Lines
A Point represents a location in space or in a drawing and has no width, height, or depth.
A Line is defined as “that which has length without breadth.” A straight line is the shortest distance between two points.
Perp Lines
Horizontal
Vertical
Indefinite
DefinitePoints
Lines
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Angles
An angle is formed by two intersecting lines.
COMPLETE CIRCLE
STRAIGHT ANGLE RIGHT ANGLE ACUTE ANGLE
OBTUSE ANGLE COMPLEMENTARY ANGLES
SUPPLEMENTARY ANGLES
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Regular Polygons
MORE THAN THREE SIDE CONSTRUCTED AROUND A CIRCLE POLYGON MAY BE INSCRIBED (POINTS TOUCH) OR
CIRCUMSCRIBED (FLATS TOUCH) ALL SIDES ARE EQUAL IN LENGTH AND IN ANGLE
INSCRIBED
CIRCUMSCRIBED
TRIANGLESQUARE
PENTAGONHEXAGON OCTAGON
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Polygons …
ANGLES IN REGULAR POLYGONS ARE FOUND BY DIVIDING A CIRCLE (3600) BY THE NUMBER OF SIDE
Except a triangle, then we use 1800
E.g. Hexagon has 6 sides. 360/6=60. Therefore we use a 600 triangle to complete a hexagon
Circumscribed Inscribed
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Creating a Perpendicular Bisecting Line..
Bisect = 2 equal parts Perpendicular = 90o to its counterpart From each end of the given line, draw an arc that is greater
than half Connect the two intersections from each of the created arcs
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Using a ruler to divide…Dividing 6 equal spaces
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Dividing a given space..
Dividing horizontal space Place ruler so that it touches each end at a number
that you can divide. Put dots on those points Draw vertical lines through those dots
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Dividing a given space vertically
Dividing vertical space Place ruler so that it touches the top
and bottom line at a number that you can divide.
Put dots on those points Draw horizontal lines through those
dots
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Tangent Lines
A line that touches a circle or arc in a point of tangency.
Is this tangent?
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Creating a tangent arcs and circles
radius
Draw a line the distance of the radius away from the given line (the line we want to be tangent to) then create a circle using the radius line to mark
the center of the circle
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Creating a circle or arc to two given lines
R
R
Draw a line the distance of the radius away from each given line. Where the two lines cross, that is
where you will place the middle of the circle.
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Creating a circle or arc to a line and an arc.
R
R•Create a line tangent to the given straight.
•Mark the radius away from the edge of the circle you want to be tangent to.
•Draw an arc from the given circle’s mid-point that represents a distance of the radius away from the edge
•Draw the circle using the point of crossing as the mid-point
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Handout: Arcs tangent to a circle and a line.
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Handout: Exclusive Arcs…..
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Handout: Inclusive Arcs
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Homework
Worksheets Exercise 3.14 Figure 4.76 (handout) Exercise 3.12
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Figure 3.14
Find center and draw the outer circle.
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Figure 3.14
Add the centerlines for the 6 circles @ 600 between each
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Figure 3.14
Draw in the 6 needed circles
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Figure 3.14
Mark lines at 150 increments
Draw teeth so that each line intersects the next at 900
Each line is at 90o to the next
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Figure 3.14
Finish with the hub and keyway
Darken final object and leave construction lines of they are light
Add border and title block
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Questions?
Remember that all drawings are done in a formal sketch fashion.. That means to sketch with some aides, and that there is some built in assumption of error for accuracy, but not concepts….
Earn 15 points extra credit by completing the 6 page handout out marked Chapter 5: Geometric Construction.