Chapter 3 – Perpendicular and Parallel LinesThe 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

Identify relationships between Lines

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

The “What” and the “Why”Prove that Lines are Parallel

Use properties of parallel lines- Scientific applications such as paths of light, reflection, and refractionUse Slope in a coordinate plane to determine if lines are parallel- Introduction to the concepts of coordinate geometryWrite an equation of a line parallel to a given line in a coordinate plane- Foundation for writing coordinate proofsUse Slope to decide if lines in a coordinate plane are perpendicular-Solving real life problems regarding the determining of right angle formationsWrite an equation of a line perpendicular to a given line.

Perpendicular and Parallel LinesSailboats 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?

1 45*

45*

Wind Wind