# Geometric Construction

## Presentation on theme: "Geometric Construction"— Presentation transcript:

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.

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

Triangles

Angles

Points and Lines