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**Geometric Construction**

Stephen A. Jung Sierra College

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**Points and Lines Plane – is defined as:**

Point – represents a location in space or on a drawing 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 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 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 (360o) A degree is divided into 60 minutes (60’) A minute is divided into 60 seconds (60”) Example: 54o 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 180o. Types of triangles:

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Quadrilaterals A quadrilateral is a plane figure bounded by four straight sides. 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.

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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 Given line A-B or Arc A-B Compass Method B A**

Midpoint of line Construction circles have the same diameter and the radius is equal to more than ½ the length of the line.

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**Bisecting an Angle Given angle A-B-C Compass Method C Equal Angles R A**

Bisector B Initial construction circle drawn at any convenient radius. Second and third circles radius equal to first.

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**Transferring an Angle Compass Method Z’ Z Equal Angles r’ r=r’**

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

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**Drawing a Triangle with sides given.**

F E D D E F Measure length of each side given. Construct circles from end points of base.

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**Drawing a Right Triangle with only two sides given**

M N R=M R= 1/2 N M N Measure length of each side given. Construct base segment N. Construct a circle = M from one end point of base.

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**Drawing an Equilateral Triangle**

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

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**Drawing Regular Polygons using CAD**

Required information prior to the construction of a polygon: Number of sides Center location Radius of the polygon Inscribed in a circle or Circumscribed about a circle R R Sides = 6 Sides = 6 Inscribed Circumscribed

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Tangents

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**Drawing a Circle Tangent to a Line**

Center of Circle G 90o Tangent Point Offset Given Radius Given Line

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**Drawing a Tangent to Two Circles**

Tangent Points C1 C2 T Tangent Points T C1 C2 T T

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**Tangent to Two Arcs or Circles**

Only One Tangent Point C1 C2

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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: Radius of the desired Arc = R Offset R R R Offset Given Right Angle

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**Drawing Tangent Arcs: Acute & Obtuse Angles**

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

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**Arc Tangent to: an Arc and a Straight Line**

Offset RG+RD Required information prior to the construction of an Arc Tangent to a line & Arc: Radius of the desired Arc = RD Given Arc T RG Offset RD RD T Given Line

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**Arc Tangent to: an Arc and a Straight Line**

Required information prior to the construction of an Arc Tangent to a line & Arc: Radius of the desired Arc = RD Given Arc Offset RG-RD RG T Offset RD RD T Given Line

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Arc Tangent to two Arcs Required information prior to the construction of an Arc Tangent to a line & Arc: Radius of the desired Arc = RD Offset Offset RG+RD RG’+RD T RG T RG’ RD Given Arcs

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**Arc Tangent to two Arcs cont.**

Required information prior to the construction of an Arc Tangent to Two Arcs: Radius of the desired Arc = RD Offset RG+RD RG Offset RG’-RD T Given Arcs RD RG’ T

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**Arc Tangent to Two Arcs cont. Enclosing Both**

Required information prior to the construction of an Arc Tangent to Two Arcs: Radius of the desired Arc = RD RD T RG’ RG T RD-RG’ RD-RG Given Arcs

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**Arc Tangent to Two Arcs & Enclosing One**

Required information prior to the construction of an Arc Tangent to Two Arcs: Radius of the desired Arc = RD Given Arcs RD RG’ RG T RD-RG’ Offset RD+RG

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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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Definitions and Examples of Geometric Terms

Definitions and Examples of Geometric Terms

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