Career & Technical Education Drafting – Product Design & Architecture Geometric...

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