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## Class Details

- 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.
- Version:
- 1.0
- Difficulty:
- Beginner
- Number of Lessons:
- 18
- Additional Language:
- Spanish, Chinese
- Related 2.0 Class:
- Geometry: Lines and Angles 151

## 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

## 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.

## Job Roles

- Assembly Mechanic
- Master Mechanic
- Autoclave Technician
- Automated Fiber Placement / Automated Tape Layup
- Composite Fundamentals
- Composite Repair Technician
- Composites Cutter and Kitting
- Filament Winding Operator
- Hot Press / Compression Mold Operator
- Infusion Operator
- Manual Layup Technician
- Manual Sprayup Technician
- Pultrusion Operator
- Trim, Drill and Finishing Technician
- Die Maker
- Electron Beam Welding Operator
- Fundamentals
- Hydroforming Operator
- Laser Cutter Operator
- Laser Welding Operator
- Lead Press Operator/Setup
- Press Brake Operator
- Roll Forming Operator
- Stamping Press Operator
- Tube/Bar Bending Operator
- Waterjet Operator
- CNC Programmer
- Grinding Technician
- Lathe Operator
- Machining Fundamentals
- Mill Operator
- Production Grinder
- Production Machinist
- Quality Technician
- Toolmaker / Diemaker
- Waterjet Operator
- Wire EDM Operator
- Automation (Motion Control, Robotics) Technician
- Electrical Maintenance Technician
- Fluid Systems Technician
- Mechanical Maintenance Technician
- Blow Mold Material Handler
- Blow Mold Operator
- Blow Mold Setup Person
- Blow Mold Technician
- Compression Mold Material Handler
- Compression Mold Operator
- Compression Mold Setup Person
- Compression Mold Technician
- Extrusion Material Handler
- Extrusion Operator
- Extrusion Setup Person
- Extrusion Technician
- Fundamentals
- Injection Mold Material Handler
- Injection Mold Operator
- Injection Mold Setup Person
- Mold Maker

## Certifications

SME- CMfgT

- CNC Lathe Operations
- CNC Milling Operations
- Metalforming I

- MSSC Quality Practices and Measurement

## Glossary

Vocabulary Term | Definition |
---|---|

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. |