Perpendicular and Parallel Lines

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Presentation transcript:

Perpendicular and Parallel Lines Chapter 3 Perpendicular and Parallel Lines

Section 5 Using Properties of Parallel Lines

GOAL 1: Using Parallel Lines in Real Life When a team of rowers competes, each rower keeps his or her oars parallel to the adjacent rower’s oars. If any two adjacent oars on the same side of the boat are parallel, does this imply that any two oars on that side are parallel? This question is examined below. Example 1 justified Theorem 3.11, and you will prove Theorem 3.12 in Exercise 38.

Example 1: Proving Two Lines are Parallel Lines m, n, and k represent three of the oars above. m || n and n || k. Prove that m || k.

Example 2: Explaining Why Steps are Parallel In the diagram at the right, each step is parallel to the step immediately below it and the bottom step is parallel to the floor. Explain why the top step is parallel to the floor.

Example 3: Building a CD Rack You are building a CD rack Example 3: Building a CD Rack You are building a CD rack. You cut the sides, bottom, and top so that each corner is composed of two 45° angles. Prove that the top and bottom front edges of the CD rack are parallel.

GOAL 2: Constructing Parallel Lines To construct parallel lines, you first need to know how to copy an angle.

In Chapter 4, you will learn why the Copying an Angle construction works. You can use the Copying an Angle construction to construct two congruent corresponding angles. If you do, the sides of the angles will be parallel.

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