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hsm12gmse_0304.pdf - 3-4 Parallel and Perpendicular Lines...

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164Chapter 3Parallel and Perpendicular Lines3-4Parallel andPerpendicular LinesObjectiveTo relate parallel and perpendicular linesJude and Jasmine leave school together to walk home. Then Jasminecuts down a path from Schoolhouse Road to get to Oak Street andJude cuts down another path to get to Court Road. Below is a diagramof the route each follows home. What conjecture can you make aboutOak Street and Court Road? Explain.Look at the givenangle markings.What do theytell you?SchoolSchool house RoadOak StreetCourt RoadTheorem 3-8TheoremIf two lines are parallel tothe same line, then they areparallel to each other.If . . .a3bandb3cThen . . .a3cabcIn the Solve It, you likely made your conjecture about Oak Street and Court Road basedon their relationships to Schoolhouse Road. In this lesson you will use similar reasoningto prove that lines are parallel or perpendicular.Essential UnderstandingYou can use the relationships of two lines to a thirdline to decide whether the two lines are parallel or perpendicular to each other.You will prove Theorem 3-8 in Exercise 7.Content StandardG.MG.3Apply geometric methods to solve designproblems.MATHEMATICALPRACTICES
Problem 1Got It?Lesson 3-4Parallel and Perpendicular Lines165Notice that Theorem 3-9 includes the phrasein a plane. In Exercise 17, you willconsider why this phrase is necessary.Proof of Theorem 3-9Given:In a plane,r'tands't.Prove:r3sProof:/1 and/2 are right angles by the definition ofperpendicular. So,/1>/2. Since corresponding anglesare congruent,r3s.Solving a Problem With Parallel Lines

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Term
Fall
Professor
NoProfessor
Tags
Cartesian Coordinate System, Perpendicular Transversal Theorem

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