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Lesson 10.1 Skills Practice 1DPH _______________________________________________________ 'DWH _________________________ Location, Location, Location! Line Relationships Vocabulary Write the term or terms from the box that best complete each statement. intersecting lines perpendicular lines parallel lines coplanar lines skew lines coincidental lines 1. are lines that lie in the same plane and do not intersect. 2. are lines in a plane that cross or intersect each other. are lines that have equivalent linear equations and overlap at every point 3. when they are graphed. 4. are lines that intersect at a right angle. 5. are lines that do not lie in the same plane. 6. are lines that lie in the same plane. Problem Set Describe each sketch using the terms intersecting lines, perpendicular lines, parallel lines, coplanar lines, skew lines, and coincidental lines. More than one term may apply. 2. © 2011 Carnegie Learning 1. perpendicular lines, intersecting lines, coplanar lines Chapter 10 Skills Practice • 711 Lesson 10.1 Skills Practice page 2 3. 4. 5. 6. Sketch an example of each relationship. 7. parallel lines © 2011 Carnegie Learning 8. coplanar lines 712 • Chapter 10 Skills Practice Lesson 10.1 Skills Practice page 3 1DPH _______________________________________________________ 'DWH _________________________ 9. intersecting lines 11. coincidental lines 10. perpendicular lines 12. skew lines Choose the description from the box that best describes each sketch. Case 1: Two or more coplanar lines intersect at a single point. Case 2: Two or more coplanar lines intersect at an infinite number of points. Case 3: Two or more coplanar lines do not intersect. © 2011 Carnegie Learning Case 4: Two or more are not coplanar. 13. 14. Case 2 Chapter 10 Skills Practice • 713 Lesson 10.1 Skills Practice page 4 16. 17. 18. © 2011 Carnegie Learning 15. 714 • Chapter 10 Skills Practice Lesson 10.1 Skills Practice page 5 1DPH _______________________________________________________ 'DWH _________________________ Use the map to give an example of each relationship. N 19. intersecting lines W E S Magnolia Drive South Daisy Lane North Daisy Lane Cherry Street Plum Street Ivy Lane Chestnut Street 20. perpendicular lines Answers will vary. © 2011 Carnegie Learning Ivy Lane and Plum Street 21. parallel lines 22. skew lines 23. coincidental lines 24. coplanar lines Chapter 10 Skills Practice • 715 © 2011 Carnegie Learning 716 • Chapter 10 Skills Practice Lesson 10.2 Skills Practice 1DPH________________________________________________________ 'DWH _________________________ When Lines Come Together Angle Relationships Formed by Two Intersecting Lines Vocabulary Match each definition to its corresponding term. 1. Two adjacent angles that form a straight line a. supplementary angles 2. Two angles whose sum is 180 degrees b. linear pair of angles Problem Set © 2011 Carnegie Learning Sketch an example of each relationship. 1. congruent figures 2. congruent angles 3. adjacent angles 4. vertical angles Chapter 10 Skills Practice • 717 Lesson 10.2 Skills Practice 5. linear pair page 2 6. supplementary angles Willow Drive Use the map to give an example of each relationship. 1 2 5 9 10 15 6 11 16 4 7 8 Main Street 13 14 Franklin Drive 12 17 3 18 19 20 21 24 Si xth 7. congruent angles Av e 8. vertical angles /3 and /4 9. supplementary angles 11. adjacent angles 718 • Chapter 10 10. linear pair 12. vertical angles Skills Practice Fif th Av e © 2011 Carnegie Learning 22 23 Lesson 10.2 Skills Practice page 3 1DPH________________________________________________________ 'DWH _________________________ Complete each sketch. 13. Draw /2 adjacent to /1. 1 2 14. Draw /2 such that it forms a vertical angle with /1. 1 15. Draw /2 such that it supplements /1 and does not share a common side. 155° © 2011 Carnegie Learning 16. Draw /2 adjacent to /1. 1 Chapter 10 Skills Practice • 719 Lesson 10.2 Skills Practice page 4 17. Draw /1 such that it forms a vertical angle with /2. 2 18. Draw /2 such that it forms a linear pair with /1. 1 Determine each unknown angle measure. 19. If /1 and /2 form a linear pair and m/1 5 42°, what is m/2? m/1 1 m/2 5 180 x 5 138 m/2 5 138° 720 • Chapter 10 Skills Practice © 2011 Carnegie Learning 42 1 x 5 180 Lesson 10.2 Skills Practice page 5 1DPH________________________________________________________ 'DWH _________________________ 20. If /1 and /2 are supplementary angles and m/1 5 101°, what is m/2? 21. If /1 and /2 form a linear pair and m/1 is one-fifth m/2, what is the measure of each angle? © 2011 Carnegie Learning 22. If /1 and /2 are supplementary angles and m/1 is 60° less than m/2, what is the measure of each angle? Chapter 10 Skills Practice • 721 Lesson 10.2 Skills Practice page 6 23. If /1 and /2 form a linear pair and m/1 is three times m/2, what is the measure of each angle? 24. If /1 and /2 are supplementary angles and m/1 is 12° more than m/2, what is the measure of © 2011 Carnegie Learning each angle? 722 • Chapter 10 Skills Practice Lesson 10.3 Skills Practice 1DPH________________________________________________________ 'DWH _________________________ Crisscross Applesauce Angle Relationships Formed by Two Lines Intersected by a Transversal Vocabulary Write the term from the box that best completes each sentence. transversal same-side interior angles alternate interior angles alternate exterior angles same-side exterior angles are pairs of angles formed when a third line (transversal) 1. intersects two other lines. These angles are on opposite sides of the transversal and are outside the other two lines. 2. A is a line that intersects two or more lines. are pairs of angles formed when a third line (transversal) 3. intersects two other lines. These angles are on the same side of the transversal and are outside the other two lines. are pairs of angles formed when a third line (transversal) 4. intersects two other lines. These angles are on opposite sides of the transversal and are in between the other two lines. are pairs of angles formed when a third line (transversal) 5. © 2011 Carnegie Learning intersects two other lines. These angles are on the same side of the transversal and are in between the other two lines. Chapter 10 Skills Practice • 723 Lesson 10.3 Skills Practice page 2 Problem Set 1. Transversal 2. Alternate interior angles 3. Alternate exterior angles 4. Same-side interior angles 5. Same-side exterior angles 6. Corresponding angles 724 • Chapter 10 Skills Practice © 2011 Carnegie Learning Sketch an example of each. Lesson 10.3 Skills Practice page 3 1DPH________________________________________________________ 'DWH _________________________ Use the map to give an example of each type of relationship. Taylor Ave 1 3 4 5 6 2 7 8 9 10 15 e Dr onro 11 Polk Way 19 21 22 7. transversal 20 17 18 14 13 23 24 27 28 25 26 29 30 Hoover Ave Roosevelt Ave 12 Wilson Ave M 16 8. alternate interior angles Hoover Ave. is a transversal that intersects Monroe Dr. and Polk Way. © 2011 Carnegie Learning 9. alternate exterior angles 11. same-side exterior angles 10. same-side interior angles 12. corresponding angles Chapter 10 Skills Practice • 725 Lesson 10.3 Skills Practice page 4 Complete each statement with congruent or supplementary. 13. The alternate interior angles formed when two parallel lines are intersected by a transversal congruent . are 14. The same-side interior angles formed when two parallel lines are intersected by a transversal . are 15. The alternate exterior angles formed when two parallel lines are intersected by a transversal . are 16. The same-side exterior angles formed when two parallel lines are intersected by a transversal . are Determine the measure of all the angles in each. 17. 152° 28° 28° 152° 28° 18. 28° 152° 152° 4x° © 2011 Carnegie Learning x° 726 • Chapter 10 Skills Practice Lesson 10.3 Skills Practice page 5 1DPH________________________________________________________ 'DWH _________________________ 19. 20. x° 2 20 x° ,3 ,4 75° ,1 © 2011 Carnegie Learning ,2 Chapter 10 Skills Practice • 727 Lesson 10.3 Skills Practice page 6 22. Solve for the value of x given 21. Solve for the value of x and y that ℓ1 i ℓ2. given that ℓ1 i ℓ2. ,1 ,2 x° ,1 66° x° 55° 125° ,2 © 2011 Carnegie Learning y° 728 • Chapter 10 Skills Practice Lesson 10.4 Skills Practice 1DPH________________________________________________________ 'DWH _________________________ Parallel or Perpendicular? Slopes of Parallel and Perpendicular Lines Vocabulary Define each term in your own words. 1. Reciprocal 2. Negative reciprocal Problem Set Determine the slope of a line parallel to the given line represented by each equation. 1. y 5 6x 1 12 2x 2 5 2. y 5 __ 3 The slope of the line is 6, so the © 2011 Carnegie Learning slope of a line parallel to it is 6. 3. y 5 8 2 5x 1x 4. y 5 14 2 __ 4 Chapter 10 Skills Practice • 729 Lesson 10.4 Skills Practice 5. 3x 1 4y 5 24 page 2 6. 15x 2 5y 5 40 Identify the slope of the line represented by each equation to determine which equations represent parallel lines. 7. a. y 5 8x 2 5 b. y 5 7 2 8x slope 5 8 slope 5 28 c. y 5 4 1 8x slope 5 8 8. a. y 5 6 2 3x b. y 5 23x 2 8 c. y 5 3x 1 10 9. a. 5y 5 220x 2 45 b. 2y 5 4x 1 6 c. 4y 5 32 2 16x 730 • Chapter 10 Skills Practice © 2011 Carnegie Learning The equations (a) and (c) represent parallel lines. Lesson 10.4 Skills Practice page 3 1DPH________________________________________________________ 'DWH _________________________ b. 2y 5 8 1 4x c. 3y 5 6x 1 18 11. a. 3x 1 5y 5 60 b. 6x 1 10y 5 240 c. 15x 1 9y 5 18 © 2011 Carnegie Learning 10. a. 4y 5 4x 2 16 Chapter 10 Skills Practice • 731 Lesson 10.4 12. a. 2x 1 8y 5 24 Skills Practice b. 232x 1 4y 5 12 page 4 c. 240x 1 5y 5 10 13. 5 14. 27 3 15. __ 4 1 17. __ 7 2 18. 2__ 5 1 2__ 5 5 16. 2__ 8 732 • Chapter 10 Skills Practice © 2011 Carnegie Learning Determine the negative reciprocal of each number. Lesson 10.4 Skills Practice page 5 1DPH________________________________________________________ 'DWH _________________________ Determine the slope of a line perpendicular to the given line represented by each equation. 19. y 5 13x 1 22 20. y 5 5x 2 17 The slope of the line is 13, so the slope 1 of a line perpendicular to it is 2___ . 13 1x 22. y 5 9 2 __ 3 23. 5x 1 6y 5 36 24. 4x 2 3y 5 21 © 2011 Carnegie Learning 1x 1 4 21. y 5 __ 6 Chapter 10 Skills Practice • 733 Lesson 10.4 Skills Practice page 6 Identify the slope of the line represented by each equation to determine which equations represent perpendicular lines. 3x 2 1 b. y 5 __ 2 2x 2 8 25. a. y 5 __ 3 __ __ slope 5 3 2 slope 5 2 3 3 x 1 14 c. y 5 2__ 2 __ slope 5 2 3 2 The equations (a) and (c) represent perpendicular lines. 1x b. y 5 18 1 __ 5 c. y 5 5x 1 31 27. a. 26y 5 24x 1 12 b. 2y 5 3x 1 8 c. 29y 5 6x 1 9 © 2011 Carnegie Learning 26. a. y 5 25x 2 23 734 • Chapter 10 Skills Practice Lesson 10.4 Skills Practice page 7 1DPH________________________________________________________ 'DWH _________________________ b. 5y 5 x 1 15 c. 4y 5 20x 2 24 29. a. 26x 1 2y 5 20 b. 29x 2 3y 5 218 c. x 1 3y 5 15 © 2011 Carnegie Learning 28. a. 25y 5 25x 1 55 Chapter 10 Skills Practice • 735 Lesson 10.4 Skills Practice 30. a. 3x 1 18y 5 272 b. 30x 1 5y 5 25 page 8 c. 22x 1 12y 5 224 Determine whether the lines described by the equations are parallel, perpendicular, or neither. 31. y 5 5x 1 8 y 5 4 1 5x slope 5 5 slope 5 5 32. y 5 15 2 2x 1 x 1 17 y 5 __ 2 1x 1 5 33. y 5 __ 3 y 5 3x 2 2 736 • Chapter 10 Skills Practice © 2011 Carnegie Learning The slopes are equal, so the lines are parallel. Lesson 10.4 Skills Practice page 9 1DPH________________________________________________________ 'DWH _________________________ 220x 1 5y 5 40 35. 3x 1 2y 5 2 2x 1 3y 5 3 © 2011 Carnegie Learning 34. 3x 1 12y 5 24 Chapter 10 Skills Practice • 737 Lesson 10.4 Skills Practice 212x 1 20y 5 160 © 2011 Carnegie Learning 36. 10y 5 6x 1 80 page 10 738 • Chapter 10 Skills Practice Lesson 10.5 Skills Practice 1DPH________________________________________________________ 'DWH _________________________ Up, Down, and All Around Line Transformations Vocabulary Write a definition for the term in your own words. 1. Triangle Sum Theorem Problem Set Sketch the translation for each line. 1. Vertically translate line AB 4 units to create line CD. Calculate the slope of each line to determine if the lines are parallel. 8 6 D C 4 2 –8 –6 –4 –2 B A 2 4 6 –2 © 2011 Carnegie Learning _______ 321 5 ______ 622 2 5 __ 4 y 2y line CD: m 5 _______ x 2x 725 5 ______ 622 2 5 __ y 2y line AB: m 5 x2 2 x1 2 1 y –4 –6 –8 8 x 2 1 2 1 4 Line AB is parallel to line CD. Chapter 10 Skills Practice • 739 Lesson 10.5 Skills Practice page 2 2. Vertically translate line AB 28 units to create line CD. Calculate the slope of each line to determine if the lines are parallel. y B 8 6 A 4 2 –8 –6 –4 –2 2 4 6 8 x –2 –4 –6 –8 3. Horizontally translate line AB 25 units to create line CD. Calculate the slope of each line to determine if the lines are parallel. y 8 6 4 2 –8 –6 A –4 –2 B 2 4 6 8 –4 –6 –8 740 • Chapter 10 x © 2011 Carnegie Learning –2 Skills Practice Lesson 10.5 Skills Practice page 3 1DPH________________________________________________________ 'DWH _________________________ 4. Horizontally translate line AB 6 units to create line CD. Calculate the slope of each line to determine if the lines are parallel. y 8 6 4 2 –8 –6 –4 B –2 2 4 6 8 x –2 A –4 –6 –8 5. Vertically translate line AB 7 units to create line CD. Calculate the slope of each line to determine if the lines are parallel. y 8 6 © 2011 Carnegie Learning 4 2 A –8 –6 –4 –2 2 4 6 8 x –2 –4 B –6 –8 Chapter 10 Skills Practice • 741 Lesson 10.5 Skills Practice page 4 6. Horizontally translate line AB 23 units to create line CD. Calculate the slope of each line to determine if the lines are parallel. y 8 6 4 2 A –8 –6 –4 –2 2 4 6 8 x –2 –4 B –6 –8 Sketch the rotation for each line. 7. Use point A as the point of rotation and rotate line AB 908 counterclockwise to form line AC. Calculate the slope of each line to determine if the lines are perpendicular. Explain how you determined your answer. _______ 523 5 ______ 522 2 5 __ 8 6 C B 4 A 2 3 –8 –6 –4 –2 2 4 6 8 x _______ 623 5 ______ 022 3 5 2 __ y 2y line AC: m 5 x2 2 x1 2 1 –2 –4 –6 –8 2 Line AB is perpendicular to line AC because the slopes are negative reciprocals of each other. 742 • Chapter 10 Skills Practice © 2011 Carnegie Learning y 2y line AB: m 5 x2 2 x1 2 1 y Lesson 10.5 Skills Practice page 5 1DPH________________________________________________________ 'DWH _________________________ 8. Use point B as the point of rotation and rotate line AB 908 clockwise to form line BC. Calculate the slope of each line to determine if the lines are perpendicular. Explain how you determined your answer. y 8 6 B 4 2 –8 –6 –4 A2 –2 4 6 8 x –2 –4 –6 –8 9. Use point A as the point of rotation and rotate line AB 908 counterclockwise to form line AC. Calculate the slope of each line to determine if the lines are perpendicular. Explain how you determined your answer. y © 2011 Carnegie Learning 8 6 4 2 A –8 –6 –4 –2 2 –2 4 6 8 x B –4 –6 –8 Chapter 10 Skills Practice • 743 Lesson 10.5 Skills Practice page 6 10. Use point B as the point of rotation and rotate line AB 908 clockwise to form line BC. Calculate the slope of each line to determine if the lines are perpendicular. Explain how you determined your answer. y 8 6 4 A –8 –6 –4 2 –2 2 4 6 8 x B –4 –6 –8 11. Use point A as the point of rotation and rotate line AB 908 clockwise to form line AC. Calculate the slope of each line to determine if the lines are perpendicular. Explain how you determined your answer. y 8 B 6 2 A –8 –6 –4 –2 2 4 6 8 –2 –4 –6 –8 744 • Chapter 10 Skills Practice x © 2011 Carnegie Learning 4 Lesson 10.5 Skills Practice page 7 1DPH________________________________________________________ 'DWH _________________________ 12. Use point B as the point of rotation and rotate line AB 908 counterclockwise to form line BC. Calculate the slope of each line to determine if the lines are perpendicular. Explain how you determined your answer. y 8 6 4 A 2 –8 –6 –4 –2 2 4 6 8 x –2 B –4 –6 –8 Reflect line segment AB over the reflection line to form line segment CD. Reflect line segment EF over the reflection line to form line segment GH. Calculate the slopes of all line segments to prove that the line segments are parallel. 13. 8 B © 2011 Carnegie Learning 6 –8 –6 –4C –2 G–2 –4 D H –6 –8 __ ___ __ ___ __ ____ __ slope of EF 5 2 5 F 4 A 2 ___ slope of AB 5 2 5 y ___ ___ AB i EF E 2 4 6 8 x slope of CD 5 5 2 slope of GH 5 5 2 ___ ____ CD i GH Chapter 10 Skills Practice • 745 Lesson 10.5 14. Skills Practice page 8 y 8 6 E A 4 2 F –8 –6 –4 –2 2 B4 6 x 8 –2 –4 –6 –8 y 15. 8 6 E 4 2 F A B –8 –6 –4 –2 2 4 6 8 x 6 8 x –2 –4 –6 –8 8 F 6 E B 4 A 2 –8 –6 –4 –2 2 4 –2 –4 –6 –8 746 • Chapter 10 Skills Practice © 2011 Carnegie Learning y 16. Lesson 10.5 Skills Practice page 9 1DPH________________________________________________________ 'DWH _________________________ 17. y 8 E 6 A 4 F B 2 –8 –6 –4 –2 2 4 6 8 x 4 6 8 x –2 –4 –6 –8 18. y 8 6 E 4 A 2 –8 F –6 –4 B –2 2 –2 –4 –6 © 2011 Carnegie Learning –8 Chapter 10 Skills Practice • 747 © 2011 Carnegie Learning 748 • Chapter 10 Skills Practice