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Geometric Construction Stephen A. Jung Sierra College

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Point – represents a location in space or on a drawing Point No height, width, or depth Represented by the intersection of two lines Short cross bar on a line, or A small point element e.g. ( + x l ) Line – is defines as “that which has length without width” 1 Line Straight Line is the shortest distance between two points Lines can be: Parallel – symbol = ll Perpendicular – symbol = Plane – is defined as: 3 points in a space 1 point and an entity with end points e.g. line or arc Points and Lines 1 Defined by Euclid

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Angles Angles are formed by two intersecting lines Common symbol = a 360 Degrees in a full circle (360 o ) A degree is divided into 60 minutes (60’) A minute is divided into 60 seconds (60”) Example: 54 o 43’ 28” is read 54 degrees, 43 minutes, and 28 seconds. Different kinds of angles are:

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Triangles A triangle is a plane figure bounded by three straight lines and the sum of the interior angles is always 180 o. Types of triangles:

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Quadrilaterals A quadrilateral is a plane figure bounded by four straight sides.quadrilateral If the opposite sides are parallel, the quadrilateral is also a parallelogram.

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Polygons A polygon is any plane figure bounded by straight lines. If the polygon has equal angles and equal sides, it can be inscribed or circumscribed around a circle, an is called a regular polygon.regular polygon

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Circles and Arcs A circle is a closed curve with all points the same distance from a point called the center. Attributes of a circle:

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Bisecting a Line or Arc B A Construction circles have the same diameter and the radius is equal to more than ½ the length of the line. Given line A-B or Arc A-B Compass Method Midpoint of line

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Bisecting an Angle Given angle A-B-C Compass Method A C B Initial construction circle drawn at any convenient radius. Second and third circles radius equal to first. Bisector Equal Angles R

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Transferring an Angle Compass Method X Z Y Initial construction circle drawn at any convenient radius. Second circle radius (R’) equal to first circle radius (R). Y’ New Location Given Angle X-Y-Z R R=R’ X’ R’ r r’ Z’ r=r’ Equal Angles

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Drawing a Triangle with sides given. Measure length of each side given. D F E D E F Construct circles from end points of base. E D

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Drawing a Right Triangle with only two sides given Measure length of each side given. M N R=M R= 1/2 N N Construct a circle = M from one end point of base. M Construct base segment N.

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Drawing an Equilateral Triangle R Given Side S R R Measure length of side given. Draw construction circles from the end points of the given side with the radius equal to that length. All angles are equal to:? 60 o

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Drawing Regular Polygons using CAD Required information prior to the construction of a polygon: 1.Number of sides 2.Center location 3.Radius of the polygon 4.Inscribed in a circle or Circumscribed about a circle R R Circumscribed Inscribed Sides = 6

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Tangents

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Drawing a Circle Tangent to a Line R G 90 o Given Radius Given Line Tangent Point Center of Circle Offset

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Drawing a Tangent to Two Circles Tangent Points C1C1 C2C2 C1C1 C2C2 T T T T

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Tangent to Two Arcs or Circles C1C1 C2C2 Only One Tangent Point

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Drawing a Tangent Arc in a Right Angle Required information prior to the construction of an Arc Tangent to a line: 1. Radius of the desired Arc = R R R R Given Right Angle Offset

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Drawing Tangent Arcs: Acute & Obtuse Angles R R R R R T T T T Acute Angle Obtuse Angle R Required information prior to the construction of an Arc Tangent to a line: Radius of the desired Arc = R Acute Angle Example Obtuse Angle Example Offset

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Arc Tangent to: an Arc and a Straight Line RGRG RDRD Given Line Required information prior to the construction of an Arc Tangent to a line & Arc: Radius of the desired Arc = R D RDRD T T Given Arc R G +R D Offset

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Arc Tangent to: an Arc and a Straight Line Given Line Required information prior to the construction of an Arc Tangent to a line & Arc: Radius of the desired Arc = R D RDRD T T RGRG Given Arc R G -R D RDRD Offset

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Arc Tangent to two Arcs Given Arcs R G’ RGRG Required information prior to the construction of an Arc Tangent to a line & Arc: Radius of the desired Arc = R D T T RDRD R G +R D R G’ +R D Offset

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Arc Tangent to two Arcs cont. R G’ RGRG Required information prior to the construction of an Arc Tangent to Two Arcs: Radius of the desired Arc = R D Given Arcs T T RDRD R G +R D R G’ -R D Offset

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Arc Tangent to Two Arcs cont. Enclosing Both RGRG R G’ Required information prior to the construction of an Arc Tangent to Two Arcs: Radius of the desired Arc = R D T T Given Arcs R D -R G R D -R G’ RDRD

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Arc Tangent to Two Arcs & Enclosing One RGRG R G’ Required information prior to the construction of an Arc Tangent to Two Arcs: Radius of the desired Arc = R D Given Arcs R D -R G’ RD+RGRD+RG RDRD T T Offset

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That’s All Folks!

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Tangent Arcs – Obtuse Angles Example

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Tangent Arcs – Acute Angles Example

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Circles and Arcs

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Polygons

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Quadrilaterals

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Triangles

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Angles

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Points and Lines

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