004.00 geometric construction

8/2/2019 004.00 Geometric Construction

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Career &

Technical

Education

Basic Geometric Terms &Construction

004.00

Explain geometric terms and applygeometric construction techniques


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Career &

Technical

Education


004.01

Explain selected geometric terms


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Geometry

The study of the size and shape ofthings

The relationship of straight and curvedlines in drawing shapes

It is essential to recognize geometry

that exists within objects for thepurpose of creating solid models or

multiview drawings


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Angles

Acute Angle Measures less than 90

Obtuse Angle Measures more than 90

Right Angle

Measures exactly 90

Vertex

Point at which two lines ofan angle intersect

Vertex


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Circle

Radius Distance from the center of a circle to its

edge

Diameter Distance across a circle through its center

Circumference Distance around the edge of a circle

Chord Line across a circle that does not pass at

the circles center


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Circle

Has 360

Quadrant

One fourth (quarter) of a circle Measures 90

Concentric

Two or more circles of differentsizes that share the same center

point

90 90

90 9

0


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Triangles

EquilateralAll three sides are of equal length

and all three angles are equal

Isosceles

Two sides are of equal length

Scalene Sides of three different lengths

and angles with three differentvalues


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Triangles

Right Triangle One of the angles equals 90

Hypotenuse The side of a right triangle that is

opposite the 90 angle

HYPOTENUSE


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Quadrilaterals

Square Four equal sides and all angles

equal 90

Rectangle

Two sides equal lengths and all

angles equal 90

Trapezoid

Only two sides are equal length


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Quadrilaterals

RhombusAll sides are equal length and

opposite angles are equal

Rhomboid

Opposite sides are equal lengthand opposite angles are equal


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Regular Polygons

Pentagon Five sided polygon

Hexagon

Six sided polygon

Octagon

Eight sided polygon


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Regular Polygons

Distance across flats Measurement across the

parallel sides of a polygon

Distance across corners

Measurement acrossadjacent corners of apolygon

FLATS

CORNERS


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Solids

Prism

Right Rectangular

Right Triangular


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Solids

Cylinder

Cone

Sphere


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Solids

Pyramid

Torus


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Geometric Terms

Circumscribe Process of creating a

polygon that fully encloses a

circle and is tangent to all ofthe polygons sides

Inscribe Process of creating a

polygon that is fully

enclosed by a circle at itscorners


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Geometric Terms

Bisect Divide into two equal

parts Tangent

A line and arc, or twoarcs that touch eachother at one point only


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Geometric Terms

Parallel Two or more lines

that are always thesame distance apart

Perpendicular

Two lines that are ata 90 angle


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Geometric Symbols

Angle

Triangle

Radius

Diameter

Parallel

Perpendicular

Square

Centerline

R

CL

C &


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Career &

Technical

Education


4.02

Demonstrate the procedures fordrawing standard geometricconstructions


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Bisect a Line w/ a Compass

Given line AB

With points A & B as centersand any radius greater than

of AB, draw arcs to intersect,creating points C & D

Draw line EF throughpoints C and D


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Bisect a Line w/ a Triangle

A B

Given lineAB

Draw line CD from

endpointA

E

F

Draw line EF fromendpoint B

C

D

G

H

Draw line GH through intersection


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Bisect an Arc

Given arc AB

With points A & B as centersand any radius greater than

of AB, draw arcs to intersect,creating points C & D

Draw line EF throughpoints C and D


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Bisect an Angle

With point O as the centerand any convenient radius R,draw an arc to intersectAO

and OB to located points Cand D

With C and D as centers

and any radius R2 greaterthan the radius of arcCD, draw two arcs tointersect, locating point E

Given angleAOB

Draw a line through points Oand E to bisect angleAOB


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Divide a Line into Equal Parts

Draw a line from endpointA perpendicular to lineAB

Position scale, placing zero on lineAC at

an angle so that the scale touches point B Keeping zero on lineAC, adjust

the angle of the scale until anyof the desired number of

divisions are included betweenlineAC and point B

Draw lines parallel to ACthrough the division marks tointersect line AB

Mark the divisions

A B

Given lineAB

C


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Construct a Hexagongiven distance Across Flats (Circumscribed)

Given distance acrossthe flats of a hexagon,draw centerlines and a

circle with a diameterequal to the distanceacross flats

With parallel edge and30 60 triangle,draw the tangents


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Construct a Hexagongiven distance Across Corners (Inscribed)

A B

D

E

C

F

Given distanceAB across the corners, draw acircle withAB as the diameter

With

Aand

Bas centersand the same radius,

draw arcs to intersect thecircle at points C, D, E,and F

Connect the points to

complete the hexagon

C t t O t


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Construct an Octagon

Across Flats (Circumscribed)

Given the distance across the flats,draw centerlines and a circle with adiameter equal to the distanceacross flats

1

2

3 4

5

6

7

8

With a parallel edge and 45triangle, draw lines tangent to

the circle in the order shownto complete the octagon

C t t O t


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Construct an Octagon

Across Corners (Inscribed)

Given the distance across thecorners, draw centerlines ABand CD and a circle with adiameter equal to thedistance across corners

Connect the points tocomplete the octagon

With the T-square and 45

triangle, draw diagonals EFand GH

A B

C

D

E

F

G

H

C t t A T t t


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Construct an Arc Tangent to

Two Lines at an Acute Angle

A

B

C

D

Given linesAB and CD

Constructparallellines

at distance R

Construct theperpendicularsto locatepoints of tangency

With O as the point,

construct the tangent arcusing distance R

R

R

O

C t t A T t t


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Two Lines at an Obtuse Angle

C

D

Given linesAB and CD

Constructparallellines

at distance R

Construct theperpendicularsto locatepoints of tangency


construct the tangent arcusing distance R

R

A

B

R

O

C t t A T t t


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Two Lines at Right Angles

Given angleABC

With D and E as thepoints, strike arcs R2equal to given radius

A

B C

R1

R2

R2

With B as the point,strike arc R1 equal

to given radius O

E

D


strike arcR

equal togiven radius

Construct an Arc Tangent to a


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Construct an Arc Tangent to a

Line and an Arc

Given lineAB and arc CD

A B

C

D

Strike arcs R1 (given radius)

R1

R1

Draw construction arc parallel togiven arc, with center O

O

Draw construction line parallel togiven lineAB

From intersection E, draw EO toget tangent point T1, and drop

perpendicular to given line to getpoint of tangency T2

E

T1

T2

Draw tangent arc RfromT1 to T2with center E



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Two Arcs

Given arcAB withcenter O and arc CDwith center S

SD

C

O

B

A

Strike arcs

R1= radius

R

R1

R1

Draw construction arcsparallel to given arcs,

using centersO

andS

Join E to O and E to S to gettangent points T

E

T

T

Draw tangent arc Rfrom T to T,with center E

R

004.00 geometric construction

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