Transcription of Parallel and Perpendicular Lines - Richard Chan
1 Prentice Hall Foundations Geometry Teaching ResourcesCopyright by Pearson Education, Inc., or its affiliates. All Rights Reserved. 35 Name Class Date 3-4 Practice Form KParallel and Perpendicular Lines 1. A developer is planning a new housing complex.! e map of the complex is shown at the that all streets lie in a plane. a. If Washington and Lincoln Streets are to be Parallel , what must be true of /1 and /2? b. Which streets must be Parallel if /3>/4? Justify your answer. c. If m/1590 and your answers to parts (a) and (b) are true, to what roads is Eagle Road Perpendicular ?
2 2. Developing Proof Copy and complete this paragraph proof of the Perpendicular Transversal ! eorem (! eorem 3-10).Given: In a plane, x'y and y 6 : x'zSince y 6 z, m/159 by the 9. By the de" nition of 9 Lines , x'9. 3. Write a paragraph : a 6 c; b 6 c; m/2565 Prove: m/1565 4. Error Analysis A classmate drew the cube at the right. He said that according to ! eorem 3 9, AB 6 CD, since they are both Perpendicular to BC. Explain your classmate s Way243xyz112abcdABEGHFDCThey must be St. and Jefferson St., Lincoln St., and Jefferson a n c and b n c, by the Transitive Property of Parallel Lines , a n b. Since l1 and the given angle are alternate interior angles, 3-9 states that the Lines must be in the same plane.
3 AB and CD are in different planes, so AB and CD are ; Corresp. ' ; zPrentice Hall Foundations Geometry Teaching ResourcesCopyright by Pearson Education, Inc., or its affiliates. All Rights Reserved. 36 Name Class Date ! e following statements describe the rungs and posts that form the back of a chair. Assume that the rungs and posts all lie in a plane. Based only on the statements, make a conclusion about the rungs, one post, or both posts of the chair back. Explain. 5. ! e rungs are Parallel and the top one is Perpendicular to the left post.
4 6. ! e right post is Perpendicular to all the rungs. 7. ! e rungs are Parallel . ! e last rung is Perpendicular to the right post and the " rst rung is Perpendicular to the left post. 8. Draw a Picture Draw the map of a town to meet the conditions below. Based on the map, explain how each street is related to the other streets. Assume that all streets lie in a plane. First Street is Parallel ! ird Street. Second Avenue is Parallel to ! ird Street. ! ird Street is Perpendicular to Main Street. Main Street is Perpendicular to North Avenue. 9. Open-Ended Cheryl is making a picture frame out of scraps of wood. List three pairs of values for x and y for which the sides of the frame will be Parallel .
5 Explain how you determined the values. 10. Reasoning Lines a, b, c, and d are in the same plane. line a is Parallel to line c. Lines b and c are Perpendicular to line d. Based on this, tell how the Lines listed below are related. Justify your answers. a. Lines a and b b. Lines a and dx y x y x x 3-4 Practice (continued) Form KParallel and Perpendicular LinesAll the rungs are'to the left post; if a line is'to one of a set of n Lines , it is'to all the n rungs are'to both posts and the posts are n to each other; if a line is'to one of a set of n Lines , it is'to all the n students work; First St., Second Ave., Third St., and North Ave. n to each other and'to Main n b; because b and c are both'to the same line , d, they are n to each other.
6 Because a n c, by the Transitive Prop. of n Lines , a n 'd; because a n b and c, and b and c'd, by the'Transversal Thm., a' may vary. Sample: 20 and 70, 30 and 60, 40 and 50; opposite sides are n if adjacent sides are'.The rungs are all n; Lines that are'to the same line are n.
