Download Bisect a Line

Career &
Technical
Drafting – Product Design & Architecture
Geometric Construction & Terms
Geometry
 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
 Acute Angle
 Measures less than 90°
 Obtuse Angle
 Measures more than 90°
 Right Angle
 Measures exactly 90°
 Vertex
Vertex
 Point at which two lines of an
angle intersect
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
circle’s center
Circle
 Has 360°
 Quadrant
 One fourth (quarter) of a circle
 Measures 90°
 Concentric
 Two or more circles of different
sizes that share the same center
point
Triangles
 Equilateral
 All 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 different values
Triangles
 Right Triangle
 One of the angles equals 90°
 Hypotenuse
 The side of a right triangle that
is opposite the 90° angle
HYPOTENUSE
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
Quadrilaterals
 Rhombus
 All sides are equal length and
opposite angles are equal
 Rhomboid
 Opposite sides are equal length and
opposite angles are equal
Regular Polygons
 Pentagon
 Five sided polygon
 Hexagon
 Six sided polygon
 Octagon
 Eight sided polygon
Regular Polygons
 Distance across flats
 Measurement across the
parallel sides of a polygon
FLATS
 Distance across corners
 Measurement across
adjacent corners of a
polygon
CORNERS
Solids
 Prism
 Right Rectangular
 Right Triangular
Solids
 Cylinder
 Cone
 Sphere
Solids
 Pyramid
 Torus
Geometric Terms
 Circumscribe
 Process of creating a polygon
that fully encloses a circle and
is tangent to all of the
polygons sides
 Inscribe
 Process of creating a polygon
that is fully enclosed by a
circle at its corners
Geometric Terms
 Bisect
 Divide into two equal
parts
 Tangent
 A line and arc, or two
arcs that touch each
other at one point
only
Geometric Terms
 Parallel
 Two or more lines that
are always the same
distance apart
 Perpendicular
 Two lines that are at a
90° angle
Geometric Symbols
Angle
Parallel
Triangle
Perpendicular
R Radius
Diameter
Square
CL Centerline
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)
1
 Given the distance across the flats,
draw centerlines and a circle with a
diameter equal to the distance
3
across flats
 With a parallel edge and 45
triangle, draw lines tangent to
the circle in the order shown
to complete the octagon
5
7
4
8
6
2
Construct an Octagon
Across Corners (Inscribed)
C
 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
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
O
 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
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