1. Drafting – Product Design & Architecture
Geometric Construction & Terms

2. 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

3. Angles Acute Angle Obtuse Angle Right Angle Vertex Vertex
Measures less than 90°
Obtuse Angle
Measures more than 90°
Right Angle
Measures exactly 90°
Vertex
Point at which two lines of an angle intersect
Vertex

4. Circle Radius Diameter Circumference Chord
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

5. Circle Quadrant Concentric Has 360° One fourth (quarter) of a circle
90°
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

6. Triangles Equilateral Isosceles Scalene
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

7. Triangles HYPOTENUSE Right Triangle Hypotenuse
One of the angles equals 90°
Hypotenuse
The side of a right triangle that is opposite the 90° angle
HYPOTENUSE

8. Quadrilaterals Square Rectangle Trapezoid
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

9. Quadrilaterals Rhombus Rhomboid
All sides are equal length and opposite angles are equal
Rhomboid
Opposite sides are equal length and opposite angles are equal

10. Regular Polygons Pentagon Hexagon Octagon Five sided polygon
Six sided polygon
Octagon
Eight sided polygon

11. Regular Polygons Distance across flats Distance across corners
Measurement across the parallel sides of a polygon
Distance across corners
Measurement across adjacent corners of a polygon

12. Solids
Prism
Right Rectangular
Right Triangular

13. Solids
Cylinder
Cone
Sphere

14. Solids
Pyramid
Torus

15. Geometric Terms Circumscribe Inscribe
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

16. Geometric Terms Bisect Tangent Divide into two equal parts
A line and arc, or two arcs that touch each other at one point only

17. Geometric Terms Parallel Perpendicular
Two or more lines that are always the same distance apart
Perpendicular
Two lines that are at a 90° angle

18. Geometric Symbols R C L Angle Triangle Radius Diameter Parallel
Perpendicular
Square
Centerline R C L

19. 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

20. Bisect a Line w/ a Triangle
Given line AB G H C D E F
Draw line CD from endpoint A A B
Draw line EF from endpoint B
Draw line GH through intersection

21. 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

22. 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

23. 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 B C
Mark the divisions
Draw lines parallel to AC through the division marks to intersect line AB

24. 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

25. Construct a Hexagon given distance Across Corners (Inscribed)
Given distance AB across the corners, draw a circle with AB as the diameter C F D E
With A and B as centers and the same radius, draw arcs to intersect the circle at points C, D, E, and F A B
Connect the points to complete the hexagon

26. 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 across flats 5 7 3 4
With a parallel edge and 45 triangle, draw lines tangent to the circle in the order shown to complete the octagon 8 6 2

27. Construct an Octagon Across Corners (Inscribed)H E F
Given the distance across the corners, draw centerlines AB and CD and a circle with a diameter equal to the distance across corners A B
With the T-square and 45° triangle, draw diagonals EF and GH
Connect the points to complete the octagon

28. Construct an Arc Tangent to Two Lines at an Acute AngleB
Given lines AB and CD
Construct parallel lines at distance R R O
Construct the perpendiculars to locate points of tangency R C D
With O as the point, construct the tangent arc using distance R

29. Construct an Arc Tangent to Two Lines at an Obtuse Angle
Given lines AB and CD
Construct parallel lines at distance R R O
Construct the perpendiculars to locate points of tangency R C D
With O as the point, construct the tangent arc using distance R

30. Construct an Arc Tangent to Two Lines at Right Angles
Given angle ABC A B
With B as the point, strike arc R1 equal to given radius R2 O E D
With D and E as the points, strike arcs R2 equal to given radius R2 R1
With O as the point, strike arc R equal to given radius C

31. 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 E T1 R1
Draw construction line parallel to given line AB O A B
From intersection E, draw EO to get tangent point T1, and drop perpendicular to given line to get point of tangency T2 T2
Draw tangent arc R from T1 to T2 with center E

32. Construct an Arc Tangent to Two Arcs
Given arc AB with center O and arc CD with center S R1 B A
Strike arcs R1 = radius R E T
Draw construction arcs parallel to given arcs, using centers O and S O R D C R1 T
Join E to O and E to S to get tangent points T S
Draw tangent arc R from T to T, with center E