Chapter 3 – Perpendicular and Parallel Lines

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. 1 45* 45* Wind Wind 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 doesn’t change direction, do you think the boats paths will ever cross?