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.)

2 160)Key VocabularyThe framework of a wooden roller coaster is composed of millionsof feet of intersecting lumber that often form Parallel Lines andtransversals. 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 and Perpendicular LinesMake this Foldable to helpyou organize information from this Chapter . Begin with onesheet of 8 12 -inch by 11-inch each side as shown.

3 Use index cards to record PerpendicularStaple or glue the outer edges to complete the and fold the long sideup 2 inches to form a in halfmatching the short sides. Reading and WritingAs you read and study the Chapter , write examples and notesabout Parallel and Perpendicular Lines on index cards. Place the cards in theappropriate 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.

4 (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.(For review, see pages 736 and 738.) 7x 12, for x 23 x 4, for x 4y 18, for x 612783456 FoldStaple or GlueFold AgainLabelChapter 3 Parallel and Perpendicular Lines125 TPQSRC hapter 3 Parallel and Perpendicular Lines125 RELATIONSHIPS BETWEEN Lines AND PLANESL ines and marecoplanar because they lie in the same plane.

5 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?

6 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 Math The term paralleland thenotation are used forlines, segments, rays, andplanes. The symbol means is not Parallel Tip 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.

7 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 .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.

8 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 .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.

9 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. 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.

10 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 . 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.