Geometric Construction Stephen A. Jung Sierra College

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

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:

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:

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

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.

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:

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.

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.

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.

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.

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.

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.

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

Tangents

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

Drawing a Tangent to Two Circles Tangent Points C1 C2 T Tangent Points T C1 C2 T T

Tangent to Two Arcs or Circles Only One Tangent Point C1 C2

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

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

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

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

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

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

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

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

That’s All Folks!

Tangent Arcs – Obtuse Angles Example

Tangent Arcs – Acute Angles Example

Circles and Arcs

Polygons

Quadrilaterals

Triangles

Angles

Points and Lines