Basic Geometric Terms & Construction

1. Basic Geometric Terms & Construction 004.00 Explain geometric terms and apply geometric construction techniques

2. Basic Geometric Terms & Construction 004.01 Explain selected geometric terms

3. 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

4. Vertex 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 intersect

5. 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

6. 90° 90° 90° 90° 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

7. 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

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

9. 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

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

11. Regular Polygons • Pentagon • Five sided polygon • Hexagon • Six sided polygon • Octagon • Eight sided polygon

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

13. Solids • Prism • Right Rectangular • Right Triangular

14. Solids • Cylinder • Cone • Sphere

15. Solids • Pyramid • Torus

16. 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

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

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

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

20. Basic Geometric Terms & Construction 4.02 Demonstrate the procedures for drawing standard geometric constructions

21. Compass Usage • LOCATE AND DRAWa center mark • MEASURE and mark radius and set compass • Compass metal point on center mark, lead at radius mark • Hold compass handle between thumb and finger • LEAN the compass forward as you rotate it

22. 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

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

24. 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

25. 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

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

27. Construct a Hexagongiven distance Across Flats (Circumscribed)prefix “circum” – around, outside,… as in circumference” • 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

28. C D A B F E Construct a Hexagongiven 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

29. 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 5 7 • With a parallel edge and 45 triangle, draw lines tangent to the circle in the order shown to complete the octagon 3 4 8 6 2

30. C G E B A H F D 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 • With the T-square and 45° triangle, draw diagonals EF and GH • Connect the points to complete the octagon

31. A R B R C D Construct an Arc Tangent to Two Lines at an Acute Angle • 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

32. A R C B R D Construct an Arc Tangent to Two Lines at an Obtuse Angle • 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

33. A D R2 R2 R1 B C E 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 O • 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

34. C R1 R1 A B O D 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 • From intersection E, draw EO to get tangent point T1, and drop perpendicular to given line to get point of tangency T2 E T1 • Draw tangent arc R from T1 to T2with center E T2

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