Transcript Bisect a Line

Career &
Technical
Basic Geometric Terms &
Construction
004.00
Explain geometric terms and apply
geometric construction techniques
Career &
Technical
Basic Geometric Terms &
Construction
004.01
Explain selected geometric terms
Geometry
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The study of the size and shape of
things
The relationship of straight and curved
lines in drawing shapes
It is essential to recognize geometry
that exists within objects for the
purpose of creating solid models or
multiview drawings
Angles
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Acute Angle
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Obtuse Angle
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Measures more than 90°
Right Angle
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Vertex
Measures less than 90°
Measures exactly 90°
Vertex
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Point at which two lines of
an angle intersect
Circle
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Radius
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Diameter
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Distance across a circle through its center
Circumference
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Distance from the center of a circle to its
edge
Distance around the edge of a circle
Chord
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Line across a circle that does not pass at
the circle’s center
Circle
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Has 360°
Quadrant
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One fourth (quarter) of a circle
Measures 90°
Concentric
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Two or more circles of different
sizes that share the same center
point
Triangles
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Equilateral
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Isosceles
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All three sides are of equal length
and all three angles are equal
Two sides are of equal length
Scalene
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Sides of three different lengths
and angles with three different
values
Triangles
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Right Triangle
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One of the angles equals 90°
Hypotenuse
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The side of a right triangle that is
opposite the 90° angle
HYPOTENUSE
Quadrilaterals
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Square
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Rectangle
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Four equal sides and all angles
equal 90°
Two sides equal lengths and all
angles equal 90°
Trapezoid
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Only two sides are equal length
Quadrilaterals
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Rhombus
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All sides are equal length and
opposite angles are equal
Rhomboid
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Opposite sides are equal length
and opposite angles are equal
Regular Polygons
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Pentagon
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Hexagon
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Five sided polygon
Six sided polygon
Octagon
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Eight sided polygon
Regular Polygons
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Distance across flats
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Measurement across the
parallel sides of a polygon
FLATS
Distance across corners
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Measurement across
adjacent corners of a
polygon
CORNERS
Solids
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Prism
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Right Rectangular
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Right Triangular
Solids
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Cylinder
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Cone
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Sphere
Solids
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Pyramid
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Torus
Geometric Terms
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Circumscribe
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Process of creating a
polygon that fully encloses a
circle and is tangent to all of
the polygons sides
Inscribe
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Process of creating a
polygon that is fully
enclosed by a circle at its
corners
Geometric Terms
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Bisect
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Divide into two equal
parts
Tangent
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A line and arc, or two
arcs that touch each
other at one point only
Geometric Terms
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Parallel
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Two or more lines
that are always the
same distance apart
Perpendicular
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Two lines that are at a
90° angle
Geometric Symbols
Angle
Parallel
Triangle
Perpendicular
R Radius
Diameter
Square
CL Centerline
Career &
Technical
Basic Geometric Terms &
Construction
4.02
Demonstrate the procedures for
drawing standard geometric
constructions
Bisect a Line w/ a Compass
 Given line AB
 With points A & B as centers
and any radius greater than ½
of AB, draw arcs to intersect,
creating points C & D
 Draw line EF through
points C and D
Bisect a Line w/ a Triangle
 Given line AB
H
F
D
 Draw line CD from
endpoint A
 Draw line EF from
endpoint B
E
B
C
A
 Draw line GH through intersection
G
Bisect an Arc
 Given arc AB
 With points A & B as centers
and any radius greater than ½
of AB, draw arcs to intersect,
creating points C & D
 Draw line EF through
points C and D
Bisect an Angle
 Given angle AOB
 With point O as the center
and any convenient radius R,
draw an arc to intersect AO
and OB to located points C
and D
 With C and D as centers
and any radius R2 greater
than ½ the radius of arc
CD, draw two arcs to
intersect, locating point E
 Draw a line through points O
and E to bisect angle AOB
Divide a Line into Equal Parts
 Given line AB
 Draw a line from endpoint A perpendicular to line AB
 Position scale, placing zero on line AC at
an angle so that the scale touches point B
 Keeping zero on line AC, adjust
the angle of the scale until any
of the desired number of
divisions are included between
line AC and point B
A
 Mark the divisions
 Draw lines parallel to AC
through the division marks to
intersect line AB
C
B
Construct a Hexagon
given distance Across Flats (Circumscribed)
 Given distance across
the flats of a hexagon,
draw centerlines and a
circle with a diameter
equal to the distance
across flats
 With parallel edge and
30° – 60 ° triangle,
draw the tangents
Construct a Hexagon
given distance Across Corners (Inscribed)
 Given distance AB across the corners, draw a
circle with AB as the diameter
 With A and B as centers
and the same radius,
draw arcs to intersect the
circle at points C, D, E,
and F
 Connect the points to
complete the hexagon
C
D
A
B
F
E
Construct an Octagon
Across Flats (Circumscribed)
 Given the distance across the flats,
draw centerlines and a circle with a
diameter equal to the distance
across flats
 With a parallel edge and 45
triangle, draw lines tangent to
the circle in the order shown
to complete the octagon
1
5
7
3
4
8
6
2
Construct an Octagon
Across Corners (Inscribed)
 Given the distance across the
corners, draw centerlines AB
and CD and a circle with a
diameter equal to the
distance across corners
 With the T-square and 45°
triangle, draw diagonals EF
and GH
 Connect the points to
complete the octagon
C
G
E
B
A
H
F
D
Construct an Arc Tangent to
Two Lines at an Acute Angle
A
 Given lines AB and CD
 Construct parallel lines
at distance R
B
O
 Construct the
perpendiculars to locate
points of tangency
 With O as the point,
construct the tangent arc
using distance R
C
D
Construct an Arc Tangent to
Two Lines at an Obtuse Angle
A
 Given lines AB and CD
 Construct parallel lines
at distance R
O
 Construct the
perpendiculars to locate
points of tangency
 With O as the point,
construct the tangent arc
using distance R
B
C
D
Construct an Arc Tangent to
Two Lines at Right Angles
 Given angle ABC
 With B as the point,
strike arc R1 equal
to given radius
A
O
D
 With D and E as the
points, strike arcs R2
equal to given radius
 With O as the point,
strike arc R equal to
given radius
B
E
C
Construct an Arc Tangent to a
Line and an Arc
 Given line AB and arc CD
 Strike arcs R1 (given radius)
 Draw construction arc parallel to
given arc, with center O
 Draw construction line parallel to
given line AB
 From intersection E, draw EO to
get tangent point T1, and drop
perpendicular to given line to get
point of tangency T2
 Draw tangent arc R from
T1 to T2 with center E
O
C
E
T1
R1
A
B
D
T2
Construct an Arc Tangent to
Two Arcs
 Given arc AB with
center O and arc CD
A
with center S
 Strike arcs R1 = radius R
 Draw construction arcs
O
parallel to given arcs,
using centers O and S
 Join E to O and E to S to get
tangent points T
 Draw tangent arc R from T to T,
with center E
E
T
BC
S
T
D