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Geometry: Lines and Angles 155

Shop Essentials Training

Class Information

Tooling U classes are offered at the beginner, intermediate, and advanced levels. The typical class consists of 12 to 25 lessons and typically requires at least two hours of instruction time.

Class Name:	Geometry: Lines and Angles 155
Description:	This class describes the properties of lines and angles and demonstrates how they are used to solve sample part drawings.
Prerequisites:	none
Difficulty:	Beginner
Number of Lessons:	18

Class Outline

Objectives
What Is Geometry?
Points, Lines, and Rays
What Is an Angle?
Types of Angles
Pairs of Angles
Perpendicular and Parallel Lines
An Intersecting Transversal
Axioms and Theorems
Intersecting Transversal: Sample Problem
Intersecting Transversal: Solution
Drilled Holes with Slots: Sample Problem
Drilled Holes with Slots: Solution
Bolt Circle: Sample Problem
Bolt Circle: Solution
Bolt Circle #2: Sample Problem
Bolt Circle #2: Solution
Summary

Class Objectives

Define geometry.
Identify the most basic forms that combine to create geometric shapes.
Define angle.
Identify common types of angles.
Identify common pairs of angles.
Define perpendicular lines.
Define parallel lines.
Identify the angles formed by a transversal intersecting two parallel lines.
Describe how the application of geometry proves statements to be true.
Describe how variables are used in geometric problems.
Solve a geometric problem using a transversal intersecting two parallel lines.
Distinguish between essential and nonessential information for solving a geometric problem.
Solve a geometric problem using a transversal intersecting two parallel lines.
Solve a geometric problem using supplemental angles.
Solve a geometric problem using supplemental and vertical angles.

Class Vocabulary
acute angle		An angle that measures more than 0° and less than 90°.
adjacent angles		Two angles that share the same vertex and one side. The two sides that are not shared form a larger angle.
alternate angles		Two angles that are located on opposite sides of an intersecting transversal.
angle		A shape formed by two rays sharing a common endpoint or two lines that intersect. An angle has one vertex and two sides.
axiom		A statement that is universally accepted as truth without proof. In geometry, axioms provide the basis for theorems.
blueprint		A document containing all the instructions necessary to manufacture a part. The key sections of a blueprint are the drawing, dimensions, and notes.
bolt circle		A number of holes with centers that are positioned around the circumference of an imaginary circle.
centerline		An imaginary line that divides a shape into two equal halves or that runs through the center of a cylindrical object.
circle		A series of points that are all the same distance from a fixed center point.
CNC programming		The creation of program codes and instructions used to run a machine tool controlled by a computer. Each unique part requires its own CNC program.
complementary angles		Two angles that, when added together, equal 90°.
computer-aided design		The use of a computer to design parts. Computer-aided design (CAD) software creates a virtual model of the part.
corresponding angles		Two angles that are located in the same relative location. If a transversal intersects two parallel lines, corresponding angles appear on the same side of the transversal.
degree		A common unit of measurement used to determine the size of an angle.
endpoint		A single point indicating where a line segment or ray ends. A ray has one endpoint, and a line segment has two endpoints.
exterior angle		An angle located outside two parallel lines or outside a closed figure.
geometry		The branch of mathematics that involves the measurements, properties, and relationships of all shapes and sizes of things.
interior angle		An angle located between two parallel lines or within a closed figure.
intersect		To meet, cut across, or overlap. Two intersecting lines form the shape of an "X."
line		A series of points that extends endlessly in two directions. A line is perfectly straight, and its length cannot be measured.
line segment		A section of a line with two endpoints that indicate where the section ends. The length of a line segment can be measured.
mathematics		The study of the measurement and relationships of things by using numbers and symbols.
obtuse angle		An angle that measures more than 90° and less than 180°.
parallel lines		Two lines in the same plane that, no matter how far they extend, do not intersect with each other. Parallel lines are the same distance apart at any given point.
perpendicular lines		Two lines that intersect to form a 90° angle.
plane		An imaginary, perfectly flat surface with no thickness that extends endlessly in all directions. Three non-linear points or two intersecting lines define the location of a plane.
point		A single, specific location. A point has no length, width or depth.
ray		A series of points that extends endlessly in one direction. A ray has one endpoint, but its length cannot be measured.
reflex angle		An angle that measures more than 180° and less than 360°.
right angle		An angle that measures exactly 90°.
straight angle		An angle that measures exactly 180°. A straight angle appears as a straight line.
supplementary angles		Two angles that, when added together, equal 180°.
theorem		A statement that must be proven to be true. Geometry involves the step-by-step, logical process of using true statements to prove a theorem.
transversal		A line that intersects two or more lines at different points.
variable		A symbol in a mathematical statement or drawing that represents an unknown quantity.
vertex		The point of an angle where its two sides meet.
vertical angles		Two angles that share the same vertex and are positioned directly opposite one another. Vertical angles are formed whenever two lines intersect.