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**Drafting – Product Design & Architecture**

Geometric Construction & Terms

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**Quadrilaterals Rhombus Rhomboid**

All sides are equal length and opposite angles are equal Rhomboid Opposite sides are equal length and opposite angles are equal

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**Regular Polygons Pentagon Hexagon Octagon Five sided polygon**

Six sided polygon Octagon Eight sided polygon

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**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

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Solids Prism Right Rectangular Right Triangular

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Solids Cylinder Cone Sphere

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Solids Pyramid Torus

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**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

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**Geometric Terms Bisect Tangent Divide into two equal parts**

A line and arc, or two arcs that touch each other at one point only

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**Geometric Terms Parallel Perpendicular**

Two or more lines that are always the same distance apart Perpendicular Two lines that are at a 90° angle

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**Geometric Symbols R C L Angle Triangle Radius Diameter Parallel**

Perpendicular Square Centerline R C L

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**Construct an Arc Tangent to Two Lines at an Acute Angle**

B 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

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**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

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**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

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**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

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**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

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