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

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Presentation on theme: "Career & Technical Education Drafting – Product Design & Architecture Geometric Construction & Terms."— Presentation transcript:

1 Career & Technical Education 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 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 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 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 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  Right Triangle One of the angles equals 90 °  Hypotenuse The side of a right triangle that is opposite the 90 ° angle HYPOTENUSE

8 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

9 Quadrilaterals  Rhombus 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 Five sided polygon  Hexagon Six sided polygon  Octagon Eight sided polygon

11 Regular Polygons  Distance across flats 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 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 Divide into two equal parts  Tangent A line and arc, or two arcs that touch each other at one point only

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

18 Geometric Symbols 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 AB  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

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  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 R 2 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

23 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

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) AB 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

26 Construct an Octagon Across Flats (Circumscribed)  Given the distance across the flats, draw centerlines and a circle with a diameter equal to the distance across flats  With a parallel edge and 45 triangle, draw lines tangent to the circle in the order shown to complete the octagon

27 Construct an Octagon Across 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

28 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

29 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

30 Construct an Arc Tangent to Two Lines at Right Angles  Given angle ABC  With D and E as the points, strike arcs R 2 equal to given radius A B C R1R1 R2R2 R2R2  With B as the point, strike arc R 1 equal to given radius O E D  With O as the point, strike arc R equal to given radius

31 Construct an Arc Tangent to a Line and an Arc  Given line AB and arc CD AB C D  Strike arcs R 1 (given radius) R1R1 R1R1  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 T 1, and drop perpendicular to given line to get point of tangency T 2 E T1T1 T2T2  Draw tangent arc R from T 1 to T 2 with center E

32 Construct an Arc Tangent to Two Arcs  Given arc AB with center O and arc CD with center S S D C O B A  Strike arcs R1 = radius R R1R1 R1R1  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


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