## Shop Essentials (Applied Mathematics) Training

Class Information
 Tooling U-SME classes are offered at the beginner, intermediate, and advanced levels. The typical class consists of 12 to 25 lessons and will take approximately one hour to complete.
 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. Difficulty: Beginner Number of Lessons: 18 Language: English, Spanish, Chinese

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

Vocabulary TermDefinition
An angle that measures more than 0° and less than 90°.
Two angles that share the same vertex and one side. The two sides that are not shared form a larger angle.
Two angles that are located on opposite sides of an intersecting transversal.
A shape formed by two rays sharing a common endpoint or two lines that intersect. An angle has one vertex and two sides.
A statement that is universally accepted as truth without proof. In geometry, axioms provide the basis for theorems.
A document containing all the instructions necessary to manufacture a part. The key sections of a blueprint are the drawing, dimensions, and notes.
A number of holes with centers that are positioned around the circumference of an imaginary circle.
An imaginary line that divides a shape into two equal halves or that runs through the center of a cylindrical object.
A series of points that are all the same distance from a fixed center point.
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.
Two angles that, when added together, equal 90°.
The use of a computer to design parts. Computer-aided design (CAD) software creates a virtual model of the part.
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.
A common unit of measurement used to determine the size of an angle.
A single point indicating where a line segment or ray ends. A ray has one endpoint, and a line segment has two endpoints.
An angle located outside two parallel lines or outside a closed figure.
The branch of mathematics that involves the measurements, properties, and relationships of all shapes and sizes of things.
An angle located between two parallel lines or within a closed figure.
To meet, cut across, or overlap. Two intersecting lines form the shape of an "X."
A series of points that extends endlessly in two directions. A line is perfectly straight, and its length cannot be measured.
A section of a line with two endpoints that indicate where the section ends. The length of a line segment can be measured.
The study of the measurement and relationships of things by using numbers and symbols.
An angle that measures more than 90° and less than 180°.
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.
Two lines that intersect to form a 90° angle.
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.
A single, specific location. A point has no length, width or depth.
A series of points that extends endlessly in one direction. A ray has one endpoint, but its length cannot be measured.
An angle that measures more than 180° and less than 360°.
An angle that measures exactly 90°.
An angle that measures exactly 180°. A straight angle appears as a straight line.
Two angles that, when added together, equal 180°.
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.
A line that intersects two or more lines at different points.
A symbol in a mathematical statement or drawing that represents an unknown quantity.
The point of an angle where its two sides meet.
Two angles that share the same vertex and are positioned directly opposite one another. Vertical angles are formed whenever two lines intersect.