Chapter 3

1
Chapter 3 Perpendicular and Parallel Lines

• The Bigger Picture
• -Properties of Perpendicular and Parallel Lines
• How to Write a Flow Proof Valuable Logic for
  Project Related Planning
• Foundational Skills for solving problems with
  triangles, and practical applications such as
  carpentry, engineering, physics

The What and the Why

• Prove that Lines are Parallel
• Use properties of parallel lines
• - Scientific applications such as paths of light,
  reflection, and refraction
• Use Slope in a coordinate plane to determine if
  lines are parallel
• - Introduction to the concepts of coordinate
  geometry
• Write an equation of a line parallel to a given
  line in a coordinate plane
• - Foundation for writing coordinate proofs
• Use Slope to decide if lines in a coordinate
  plane are perpendicular
• Solving real life problems regarding the
  determining of right angle formations
• Write an equation of a line perpendicular to a
  given line.

• Identify relationships between Lines
• Identify angles formed by coplanar lines
  intersected by a transversal
• Laying the foundation for work with angles and
  their proofs
• Prove and use results about perpendicular lines
• Useful application for real-life situations such
  as carpentry and construction related analysis
• Write Flow Proofs
• Learn the basics of flow diagrams in support of
  proofs. Valuable real-life tool used for project
  planning in virtually every industry
• Prove and use results about parallel lines and
  transversals
• - Understand the world around you with regard to
  intersecting lines and the angles they form

2
Perpendicular and Parallel Lines

• Sailboats are actually designed to sail against
  the wind. Most sailboats can sail at an angle of
  45 to the direction from which the wind is
  blowing. If a sailboat heads directly into the
  wind, the sail simply flaps and becomes useless.
• In the drawing to the right, what do you think
  the measure of angle 1 is based on the path in
  which both boats are traveling?
• If the boats always sail at a 45 angle to the
  wind, and the wind doesnt change direction, do
  you think the boats paths will ever cross?