Chapter 3: Parallel and Perpendicular Lines

1 Parallel andPerpendicular Lines124 Chapter 3 Parallel and Perpendicular LinesRichard Cummins/CORBIS124 Chapter 3 Parallel and Perpendicular Lines Lessons 3-1, 3-2, and 3-5 Identify anglerelationships that occur with Parallel Lines and atransversal, and identify and prove Lines parallelfrom given angle relationships. Lessons 3-3 and 3-4 Use slope to analyze a lineand to write its equation. Lesson 3-6 Find the distance between a pointand a line and between two Parallel Lines . Parallel Lines (p. 126) transversal (p. 127) slope (p. 139) equidistant (p. 160)Key VocabularyThe framework of a wooden roller coaster is composed ofmillionsof feet of intersecting lumber that often form Parallel Lines andtransversals.

2 Roller coaster designers, construction managers, andcarpenters must know the relationships of angles created by parallellines and their transversals to create a safe and stable will find how measures of angles are used in carpentry and construction in Lesson SkillsTo be successful in this Chapter , you ll need to masterthese skills and be able to apply them in problem-solving situations. Reviewthese skills before beginning Chapter Lesson 3-1 Naming SegmentsName all of the Lines that contain the given point.(For review, see Lesson 1-1.) Lessons 3-2 and 3-5 Congruent AnglesName all angles congruent to the given angle.(For review, see Lesson 1-4.)5. 26. 57. 38. 8 For Lessons 3-3 and 3-4 Equations of LinesFor each equation, find the value of yfor the given value of x.

3 (For review, see pages 736 and 738.) 7x 12, for x 23 x 4, for x 4y 18, for x 612783456 Chapter 3 Parallel and Perpendicular Lines125 TPQSRC hapter 3 Parallel and Perpendicular Lines125 Parallel and Perpendicular LinesMake this Foldable to help you organize yournotes. Begin with one sheet of 8 by 11 2 Parallel PerpendicularReading and WritingAs you read and study the Chapter , write examples and notes about Parallel andperpendicular Lines on index cards. Place the cards in the appropriate or GlueFold AgainLabelFold in half matching the short and fold the long side up 2 inches to form a or glue the outeredges to complete each side as shown. Use index cards to record BETWEEN Lines AND PLANESL ines and marecoplanar because they lie in the same plane.

4 If the Lines were extended indefinitely,they would not intersect. Coplanar Lines that do not intersect are called .Segments and rays contained within Parallel Lines are also symbol means is Parallel to. Arrows areused in diagrams to indicate that Lines are Parallel . In the figure, the arrows indicate that PQ is Parallel to RS .Similarly, two planes can intersect or be Parallel . In the photograph above, the roofs of each level are contained in . The walls and the floor of each level lie in intersecting planesPQRSPQRS Parallel linesVocabulary Parallel Lines Parallel planes skew Lines transversal consecutive interiorangles alternate exterior angles alternate interior angles corresponding anglesParallel Lines andTransversalsare Parallel Lines and planesused in architecture?

5 Are Parallel Lines and planesused in architecture?Architect Frank Lloyd Wright designedmany buildings using basic shapes, Lines ,and planes. His building at the right hasseveral examples of Parallel Lines , parallelplanes, and skew symbol means is not Parallel to. Identify the relationships between two Lines or two planes. Name angles formed by a pair of Lines and Robert Holmes/CORBISStep 1 Draw two Parallel planesto represent the top andbottom of the 2 Draw the edges. Makeany hidden edges of theprism 3 Label the a Rectangular PrismA rectangular prism can be drawn using Parallel Lines and Parallel the Parallel planes in the the planes that intersect plane ABCand name their all segments Parallel to B F.

6 126 Chapter 3 Parallel and Perpendicular LinesLesson 3-1 Parallel Lines and Transversals127 Notice that in the Geometry Activity, A E and G F do not intersect. These segmentsare not Parallel since they do not lie in the same plane. Lines that do not intersectand are not coplanar are called . Segments and rays contained in skewlines are also linesANGLE RELATIONSHIPSIn the drawing of the railroad crossing, noticethat the tracks, represented by line t,intersect the sides of the road, represented by Lines mand n. A line that intersects two or more Lines in a plane at different points is called Relationshipsa. Name all planes that are Parallel to plane CDEb. Name all segments that intersect C H.

7 B C , C D , C E , E H , and G H c. Name all segments that are Parallel to E F .A D , B C , and G H d. Name all segments that are skew to B G .A D , C D , C E , E F , and E H DAEFBHCGI dentify TransversalsAIRPORTSSome of the runways at O Hare International Airport are shownbelow. Identify the sets of Lines to which each given line is a line qIf the Lines are extended, line qintersects Lines , n, p, and line mlines , n, p, and rc. line nlines , m, p, and qd. line rlines , m, p, and qmnqrp Control TowerExample1 Example1 Example2 Example2 IdentifyingSegmentsUse the segments drawnin the figure even thoughother segments TipTransversalsThe Lines that thetransversal intersectsneed not be TipIn the drawing of the railroad crossing above, notice that line tforms eight angleswith Lines mand n.

8 These angles are given special names, as are specific pairings ofthese Chapter 3 Parallel and Perpendicular LinesTransversals and AnglesNameAnglesexterior angles 1, 2, 7, 8interior angles 3, 4, 5, 6 3 and 6, 4 and 5 1 and 7, 2 and 8 3 and 5, 4 and 6 1 and 5, 2 and 6, 3 and 7, 4 and 8corresponding anglesalternate interior anglesalternate exterior anglesconsecutive interior ENDEDDraw a solid figure with Parallel planes. Describe which parts ofthe figure are THE ERRORJ uanita and Eric are naming alternate interior angles in thefigure at the right. One of the angles must be 4. Who is correct? Explain your Describe a real-life situation in which Parallel Lines seem to Exercises 4 6, refer to the figure at the all planes that intersect plane all segments that are Parallel to C D.

9 All segments that intersect K L .DAKJBLCMC oncept CheckIdentify Angle RelationshipsRefer to the figure below. Identify each pair of angles as alternate interior,alternate exterior, corresponding, or consecutive 1 and 7b. 2 and 10alternate exteriorcorrespondingc. 8 and 9d. 3 and 12consecutive interiorcorrespondinge. 4 and 10f. 6 and 11alternate interioralternate exterior127109811345612abc Eric 4 and 10 4 and 5 Juanita 4 and 9 4 and 6127109811345612 Example3 Example3 Same SideInterior Angles Consecutive interiorangles are also called same side interior TipTransversal pintersectslines qand PracticeLesson 3-1 Parallel Lines and Transversals129 Identify the pairs of Lines to which each given line is a each pair of angles as alternate interior, alternate exterior, corresponding, or consecutive 7 and 1012.

10 1 and 513. 4 and 614. 8 and 1 Name the transversal that forms each pair of angles. Then identify the special name for the angle 3 and 1016. 2 and 1217. 8 and 14 MONUMENTSFor Exercises 18 21, refer to the photograph of the Lincoln a pair of Parallel Lines found on the Lincoln an example of Parallel a pair of skew a transversal passing through a pair of 1415161211p mq123465871091211abcqrtpFor Exercises 22 27, refer to the figure at the all segments Parallel to A B . all planes intersecting plane all segments Parallel to T U . all segments skew to D E . all planes intersecting plane all segments skew to A P .Identify the pairs of Lines to which each given line is a and ApplyPractice and ApplyAngelo Hornak/CORBIS ApplicationForExercises22 2728 3132 47 SeeExamples123 Extra Practice See page Practice See page each pair of angles as alternateinterior, alternate exterior, corresponding, or consecutive 2 and 1033.