Career & Technical
Education
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 Point at which two lines of an
angle intersectVertex
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
90° 90°
90° 90°
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
Distance across corners Measurement across
adjacent corners of a polygon
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
Triangle
Radius
Diameter
Parallel
Perpendicular
Square
Centerline
R
CL
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
A B
Given line AB
Draw line CD from endpoint A
E
F
Draw line EF from endpoint B
C
D
G
H
Draw line GH through intersection
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
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
Given angle AOB
Draw a line through points O and E to bisect angle AOB
Divide a Line into Equal Parts
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
Draw lines parallel to AC through the division marks to intersect line AB
Mark the divisions
A B
Given line AB
C
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 Hexagongiven distance Across Corners (Inscribed)
A B
D
E
C
F
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
Construct an OctagonAcross Flats (Circumscribed)
Given the distance across the flats, draw centerlines and a circle with a diameter equal to the distance across flats
1
2
3 4
5
6
7
8 With a parallel edge and
45 triangle, draw lines tangent to the circle in the order shown to complete the octagon
Construct an OctagonAcross 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
Connect the points to complete the octagon
With the T-square and 45° triangle, draw diagonals EF and GH
A B
C
D
E
F
G
H
Construct an Arc Tangent to Two Lines at an Acute Angle
A
B
C
D
Given lines AB and CD
Construct parallel lines at distance R
Construct the perpendiculars to locate points of tangency
With O as the point, construct the tangent arc using distance R
R
R
O
Construct an Arc Tangent to Two Lines at an Obtuse Angle
C
D
Given lines AB and CD
Construct parallel lines at distance R
Construct the perpendiculars to locate points of tangency
With O as the point, construct the tangent arc using distance R
R
A
B
R
O
Construct an Arc Tangent to Two Lines at Right Angles
Given angle ABC
With D and E as the points, strike arcs R2 equal to given radius
A
B C
R 1
R2
R2
With B as the point, strike arc R1 equal to given radius
O
E
D
With O as the point, strike arc R equal to given radius
Construct an Arc Tangent to a Line and an Arc
Given line AB and arc CD
A B
C
D
Strike arcs R1 (given radius)
R1
R 1
Draw construction arc parallel to given arc, with center O
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
ET1
T2
Draw tangent arc R from T1 to T2 with center E
Construct an Arc Tangent to Two Arcs
Given arc AB with center O and arc CD with center S
S D
C
OB
A
Strike arcs R1 = radius R
R1
R1
Draw construction arcs parallel to given arcs, using centers O and S
Join E to O and E to S to get tangent points T
E
T
T
Draw tangent arc R from T to T, with center E
R