ENGAGE. Daily Routines Common Core. Essential Question. Making Connections Invite students to tell you what they know about parking lots.

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1 LESSON 10.3 Parallel Lines and Perpendicular Lines LESSON T GLNE R ocus: ommon ore State Standards Learning Objective 4.G..1 raw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two dimensional figures. Identify and draw parallel lines and perpendicular lines. MTHEMTIL PRTIES (See ematical Practices in GO! in the Planning Guide for full text.) MP4 Model with mathematics. MP5 Use appropriate tools strategically. MP6 ttend to precision. R oherence: Standards cross the Grades efore Grade 4 fter 3.G..1 4.G..1 5.G..3 5.G..4 R Rigor: Level 1: Understand oncepts...share and Show ( hecked Items) Level 2: Procedural Skills and luency...on Your Own, Practice and Homework Level 3: pplications...think Smarter and Go eeper Language Objective Students discuss with a partner which tools they need to identify and draw parallel lines and perpendicular lines. Materials oard, straightedge R or more about how GO! fosters oherence within the ontent Standards and ematical Progressions for this chapter, see page 547. bout the Professional evelopment Why Teach This? In this lesson, students learn to distinguish between intersecting lines and parallel lines in a plane: intersecting lines cross at exactly one point, while parallel lines never share a common point. Parallel lines are always the same distance apart. Students also learn that perpendicular lines are intersecting lines that form four right angles. s students work through the lesson, be sure to relate the new terms to real-world examples. The language of geometry is key to describing things around us. Encourage students to draw and label figures described. reating models of parallel, perpendicular, and intersecting lines will help students later when distinguishing between parallelograms and rectangles. Professional evelopment Videos 561 hapter 10 Interactive Student Edition Personal Trainer on the Spot Video nimated Models itools: Geometry HMH Mega

2 aily Routines ommon ore Problem of the ay 10.3 In baseball, home plate is a five-sided figure with five angles. What type of angle is angle? right E 1 ENGGE with the Interactive Student Edition Essential Question How can you identify and draw parallel lines and perpendicular lines? Making onnections Invite students to tell you what they know about parking lots. What is a parking lot? parking lot is usually a rectangular shaped area with lines for people to park their cars in. Learning ctivity What is the problem the students are trying to solve? onnect the story to the problem. Vocabulary intersecting lines, parallel lines, perpendicular lines Interactive Student Edition Multimedia Glossary e Vocabulary uilder Materials Word escription (see eteacher Resources) Word escription Have students use the Word escription graphic organizer to define the new vocabulary words in this lesson and any previous terms in this chapter with which they have difficulty. rawing examples and nonexamples is important to distinguish between the different types of lines or angles. What problem are you trying to solve? ind out what kind of lines have been formed in the parking lot. If the two lines that are side by side were made longer, would they ever cross? No, the lines always stay the same distance apart What kind of angles are formed where the line that runs along the row of cars meets with the lines that the cars are parked between? right angles Literacy and ematics hoose one or more of the following activities. Have students construct a miniature parking lot in the classroom. Then have students summarize their observations. Have students discuss how a parking lot reflects the properties they know about pairs of parallel sides in rectangles. Write the definition. escribe using facts and characteristics. parallel lines How can you identify and draw parallel lines and perpendicular lines? Write or draw an example. Write or draw a nonexample. 561

3 LESSON EXPLORE Unlock the Problem MTHEMTIL PRTIES To introduce the lesson, have students watch the Real World Video, Maglev Trains. Maglev is short for magnetic levitation. Levitation means to rise in the air. MP6 ttend to precision. Review the information in the chart. How are intersecting lines and perpendicular lines the same? How are they different? Possible answer: both types of lines cross at one point, forming four angles. Only perpendicular lines form four angles that are right angles. an parallel lines ever be perpendicular? Explain. No; possible explanation: perpendicular lines intersect and parallel lines never intersect. ELL Strategy: Restate raw on the board two parallel lines. Use hand gestures as you tell students that parallel lines never intersect and never cross each other. Try This! Explain that the phrase appear to be is used because it is not possible to tell whether the streets on the map are really parallel; if they were extended, they may intersect. an more than two lines be parallel? Explain. Yes; possible explanation: if all the lines are extended, it is possible that more than two of the lines will never touch, so those lines are all parallel. re all intersecting lines perpendicular? Explain. No; possible explanation: perpendicular lines are special types of intersecting lines. Some intersecting lines that form angles are not right angles. MP4 Model with mathematics. Have students make a diagram to help explain. Two lines are perpendicular to a third line. How are the first two lines related to each other? Explain. Possible answer: the lines are parallel. My drawing shows that the two lines are always the same distance apart. Talk parallel. Use Talk to help students recognize that two rays can be Suppose two lines are parallel. an a part of each of these lines be a ray? Explain. Possible answer: yes; the part of each line from a point on the line extending in one direction is a ray. 561 hapter 10 4.G..1 raw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. Image redits: (t) ernd Mellmann/lamy Images Parallel Lines and Perpendicular Lines Parallel lines are lines in a plane that are always the same distance apart. Parallel lines or line segments never meet. In the figure, lines and, even if extended, will never meet. The lines are parallel. Write i. Lines and are also parallel. So, i. Intersecting lines cross at exactly one point. Intersecting lines that form right angles are perpendicular. In the figure, lines and are perpendicular because they form right angles at vertex. Write '. Lines and are also perpendicular. So, '. Use the figure for two sides that appear to be parallel. RV and ST 2. two sides that appear to be perpendicular. RV and RS or RS and ST 3. two sides that appear to be intersecting, but not perpendicular. RV and VT or TV and ST hapter Resources Parallel Lines and Perpendicular Lines Essential Question How can you identify and draw parallel lines and perpendicular lines? Unlock the Problem You can find models of lines in the world around you. or example, two streets that cross each other model intersecting lines. Metal rails on a train track that never cross model parallel lines. Try This! Tell how the streets appear to be related. Write perpendicular, parallel, or intersecting. W 36th St and roadway intersecting W 35th St and 7th ve intersecting, perpendicular W 37th St and W 36th St parallel T V Reteach 10-9 Reteach L R S N O M lphabet Soup Use all 26 capital letters of the alphabet. Place them into as many soups as possible. Possible answers are given. 1. Letters with parallel line segments 2. Letters with perpendicular line segments E,, H, M, N, Z 3. Letters with intersecting, but not perpendicular, line segments, K, M, N, V, W, X, Y, Z hapter Resources Talk Maglev trains use magnets to lift them above the tracks while moving. Term and efi nition raw It Read It Write It Intersecting lines are lines in a H K Line HI intersects line K HI and K intersect at plane that cross at exactly one point. at point X. point X Intersecting lines form four angles. X I Parallel lines are lines in a plane that E Line E is parallel to line E i G are always the same distance apart. G. The symbol i means is Parallel lines never intersect. parallel to. G Perpendicular lines are lines in a plane that intersect to form four right angles. Yes; possible explanation: a ray is a part of a line. If the lines the rays are part of are parallel, then the rays are parallel. Reteach 10.3 Geometry 4.G..1 MTHEMTIL PRTIES MP4, MP6, MP7 Line LM is perpendicular to line NO. W 35th St LM ' NO The symbol ' means is perpendicular to. W 37th St W 36th St 7th ve E,, H, L, T roadway MTHEMTIL PRTIES 6 Use Vocabulary an two rays be parallel? Explain. hapter ifferentiated 2 Enrich Instruction Enrich 4. Letters with no parallel, perpendicular, or intersecting line segments,,, G, I,, O, P, Q, R, S, U Enrich

4 Z Y X STEP 3: Make sure YX and YZ intersect at point Y. 1. the figure you drew. 2. an you classify the figure? Explain. ZYX is a right angle, since YX and YZ are perpendicular, Share and Show 1. raw and label QR i ST. Use the figure for 2 and ctivity raw and label Materials straightedge STEP 1: raw and label YX. STEP 2: Then draw and label YZ. STEP 4: Make sure the rays are perpendicular. ZYX and perpendicular rays form right angles. MTH OR YX ' YZ intersecting at point Y. Think: Parallel lines never intersect. Parallel line segments are parts of parallel lines. Q S Possible answers are given. 2. two line segments that appear to be parallel. and 3. two line segments that appear to be perpendicular. and Possible answer: the symbol i looks like parallel line segments, and the symbol ' looks like perpendicular line segments. R T How can you check if two rays are perpendicular? I can use a square corner to check if the rays are perpendicular. Talk MTHEMTIL PRTIES 4 Use Symbols How could the symbols ' and i help you remember which relationships they describe? ctivity Students draw two perpendicular rays to form right angle ZYX. How are rays YX and YZ related? Possible answer: they both have the same endpoint Y. What does the upside-down T symbol mean? that the rays are perpendicular What are all the ways to name the figure you drew? angle ZYX, angle XYZ, angle Y 3 If EXPLIN Share and Show MTH OR Quick heck MTH The first problem connects to the learning model. Have students use the oard to explain their thinking. Use the checked exercises for Quick heck. Students should show their answers for the Quick heck on the oard. Talk Use Talk to focus on students understanding of the symbols for perpendicular and parallel lines. What do the symbols for parallel and perpendicular look like? two parallel line segments; two perpendicular line segments a student misses the checked exercises RtI dvanced Learners Materials ruler or straightedge Visual / Kinesthetic Partners Have students draw street maps based on a description given by their partner. One student starts by drawing a horizontal line across the middle of a blank sheet of paper and labeling it Main Street. The partner then describes another street and its geometric relationship to Main Street, while the other student draws it. or example, Oak Street is above and parallel to Main Street. Have the partner describe five streets that are either perpendicular, parallel, or intersecting to another street on the map. Have partners switch roles and repeat. Then ifferentiate Instruction with Reteach 10.3 Personal Trainer 4.G..1 RtI Tier 1 ctivity (online) OMMON ERRORS Error Students may confuse perpendicular lines and parallel lines. Example or Exercise 2, students name sides and as parallel. Springboard to Learning Help students remember the meaning of parallel by underlining the pair of l s in the word, which look like parallel lines. 562

5 On Your Own If students complete the checked exercises correctly, they may continue with the remaining exercises. In Exercises 4 and 5, students identify perpendicular lines and parallel lines in a geometric figure. Have students note that lines or sides of figures can appear to be parallel or perpendicular. 4 ELORTE Problem Solving pplications MTHEMTIL PRTIES On Your Own Use the figure for a pair of lines that are perpendicular. and HG 5. a pair of lines that appear to be parallel. G raw and label the figure described. 6. RS i Possible TU 7. KL and drawings are shown. KM 8. ' E R and S T U K L 9. K ' LM 10. ST intersecting UV at point X M H 11. i G E Exercise 12 requires students to recognize that if the lines were extended, they would eventually intersect. re lines HL and IM parallel? Explain. No; possible explanation: the lines appear not to be the same distance apart. EEPER MP7 Look for and make use of structure. If a line is perpendicular to one of two parallel lines, is it perpendicular to the other line as well? Explain. Yes; possible explanation: the perpendicular line will intersect both parallel lines at right angles since the parallel lines are the same distance apart. L Use the figure for K 12. an says that HL is parallel to IM. Is an correct? Explain. No; possible explanation: if you extend the lines, they will intersect. M 13. EEPER two intersecting line segments that are not perpendicular. Possible answer: HL and LM S U X V T G G H I K L M hapter 10 Lesson hapter 10

6 MTHEMTIL PRTIES NLYZE Use the house plan at the right for What geometric term describes a corner of the living room? Possible answers: right angle or perpendicular line segments 15. three parts of the plan that show line segments. Possible answers: a wall in the master bedroom, the Kitchen ining Room Living Room amily Room athroom Master edroom edroom or Exercise 16, students must find a pair of line segments that are always the same distance apart. In the case of these house plans, opposite walls of rooms and outer walls of the house appear to be parallel. bathroom door, a wall in the dining room 16. a pair of line segments that appear to be parallel. Possible answer: two walls in the living room that do not intersect and are opposite each other on the Spot Video Tutor Use this video to help students model and solve this type of Think Smarter problem. Use the map at the right for a street that appears to be parallel to S 17th Street. on the Spot videos are in the Interactive Student Edition and at Possible answers: S 18th Street, S 19th Street, S 20th Street MTHEMTIL PRTIE 4 Use iagrams a street that appears to be parallel to Vernon Street. Perry Street 19. a street that appears to be perpendicular to S 19th Street. Possible answers: ustin Street, hestnut Street Vernon St S 19th St S 18th St S 17th St hestnut St ustin St Perry St S 20th St MP4 Model with mathematics. In Exercises 17 19, students identify and name parallel and perpendicular streets on a map. Why do you think city streets often are designed to be parallel or perpendicular? Possible answer: it is easier to navigate and to get from one place to another. 20. hoose the labels to make a true statement. 564 GH I is perpendicular to E E GH E G H I Exercise 20 assesses students application of the concept of perpendicular lines. Students who choose lines and have chosen parallel lines instead of perpendicular lines. These students may have reversed the meanings of the two terms. Students who choose line GH may not understand the concept of parallel or perpendicular lines since this line is neither parallel nor perpendicular to any lines shown in the figure. IERENTITE INSTRUTION INEPENENT TIVITIES 5 EVLUTE ormative ssessment ctivities oncentrate! Students complete orange ctivity ard 13 by matching the names of lines, angles, and twodimensional shapes to pictures. ifferentiated enters Kit ctivities Picture Perfect! Students complete orange ctivity ard 13 by matching the names of lines, angles, and twodimensional shapes to pictures. Literature Skateboarding Takes Shape Students read about how plane figures and angles are used in skateparks. Essential Question Using the Language Objective Reflect Have students discuss with a partner which tools they need to answer the Essential Question. How can you identify and draw parallel lines and perpendicular lines? Possible answer: I can use the definitions. Perpendicular lines are lines in a plane that intersect to form four right angles. Parallel lines are lines in a plane that are always the same distance apart; they never intersect. ournal WRITE raw and label an example of two parallel lines that are perpendicular to a third line. 564

7 Practice and Homework Use the Practice and Homework pages to provide students with more practice of the concepts and skills presented in this lesson. Students master their understanding as they complete practice items and then challenge their critical thinking skills with Problem Solving. Use the Write section to determine student s understanding of content for this lesson. Encourage students to use their ournals to record their answers. Parallel Lines and Perpendicular Lines Use the figure for a pair of lines that appear to be perpendicular. P M Think: Perpendicular lines form right angles. and E appear to form right angles. and E 2. a pair of lines that appear to be parallel. R and raw and label the figure described. 3. MN and PQ intersecting at 4. Possible drawings are shown. WX YZ 5. H K point R Q N W Y X Z Practice and Homework OMMON ORE STNR 4.G..1 raw and identify lines and angles, and classify shapes by properties of their lines and angles. E H K Problem Solving Use the street map for two streets that intersect but do not appear to be perpendicular. Oak and Maple or Oak and irch 7. two streets that appear to be parallel to each other. Maple and irch 8. WRITE raw and label an example of two parallel lines that are perpendicular to a third line. Elm heck students drawings. Oak Maple irch hapter hapter 10

8 Lesson heck (4.G..1) 1. Write a capital letter that appears to have perpendicular line segments? G H TEST PREP 2. In the figure, which pair of line segments appear to be parallel? ontinue concepts and skills practice with Lesson heck. Use Spiral Review to engage students in previously taught concepts and to promote content retention. ommon ore standards are correlated to each section. Possible answer: T G and H Spiral Review (4.NT..5, 4.NT..6, 4.N..2, 4.G..2) 3. Nolan drew a right triangle. How many acute angles did he draw? 4. Mike drank more than half the juice in his glass. What fraction of the juice could Mike have drunk? 2 acute angles Possible answer: 5_ 8 5. school principal ordered 1,000 pencils. He gave an equal number to each of 7 teachers until he had given out as many as possible. How many pencils were left? pencils 6. carton of juice contains 64 ounces. Ms. Wilson bought 6 cartons of juice. How many ounces of juice did she buy? 384 ounces OR MORE PRTIE GO TO THE Personal Trainer 566