Lesson 10.1 Skills Practice

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1 Lesson 10.1 Skills Practice 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.. are lines in a plane that cross or intersect each other. 3. are lines that have equivalent linear equations and overlap at every point when they are graphed.. 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. 1.. perpendicular lines, intersecting lines, coplanar lines Chapter 10 Skills Practice 711

2 Lesson 10.1 Skills Practice page Sketch an example of each relationship. 7. parallel lines. coplanar lines 71 Chapter 10 Skills Practice

3 Lesson 10.1 Skills Practice page 3 9. intersecting lines 10. perpendicular lines 11. coincidental lines 1. 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 : Two or more coplanar lines intersect at an infinite number of points. Case 3: Two or more coplanar lines do not intersect. Case : Two or more are not coplanar Case Chapter 10 Skills Practice 713

4 Lesson 10.1 Skills Practice page Chapter 10 Skills Practice

5 Lesson 10.1 Skills Practice page 5 Use the map to give an example of each relationship. N Cherry Street W E North Daisy Lane S South Daisy Lane Magnolia Drive Ivy Lane Plum Street Chestnut Street 19. intersecting lines Answers will vary. 0. perpendicular lines Ivy Lane and Plum Street 1. parallel lines. skew lines 3. coincidental lines. coplanar lines Chapter 10 Skills Practice 715

6 716 Chapter 10 Skills Practice

7 Lesson 10. Skills Practice 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. Two angles whose sum is 10 degrees b. linear pair of angles Problem Set Sketch an example of each relationship. 1. congruent figures. congruent angles 3. adjacent angles. vertical angles Chapter 10 Skills Practice 717

8 Lesson 10. Skills Practice page 5. linear pair 6. supplementary angles Use the map to give an example of each relationship. Willow Drive Main Street Franklin Drive Sixth Ave 1 3 Fifth Ave 7. congruent angles. vertical angles /3 and / 9. supplementary angles 10. linear pair 11. adjacent angles 1. vertical angles 71 Chapter 10 Skills Practice

9 Lesson 10. Skills Practice page 3 Complete each sketch. 13. Draw / adjacent to / Draw / such that it forms a vertical angle with / Draw / such that it supplements /1 and does not share a common side Draw / adjacent to /1. 1 Chapter 10 Skills Practice 719

10 Lesson 10. Skills Practice page 17. Draw /1 such that it forms a vertical angle with /. 1. Draw / such that it forms a linear pair with /1. 1 Determine each unknown angle measure. 19. If /1 and / form a linear pair and m/1 5, what is m/? m/1 1 m/ x 5 10 x 5 13 m/ Chapter 10 Skills Practice

11 Lesson 10. Skills Practice page 5 0. If /1 and / are supplementary angles and m/ , what is m/? 1. If /1 and / form a linear pair and m/1 is one-fifth m/, what is the measure of each angle?. If /1 and / are supplementary angles and m/1 is 60 less than m/, what is the measure of each angle? Chapter 10 Skills Practice 71

12 Lesson 10. Skills Practice page 6 3. If /1 and / form a linear pair and m/1 is three times m/, what is the measure of each angle?. If /1 and / are supplementary angles and m/1 is 1 more than m/, what is the measure of each angle? 7 Chapter 10 Skills Practice

13 Lesson 10.3 Skills Practice 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 alternate interior angles alternate exterior angles same-side interior angles same-side exterior angles 1. are pairs of angles formed when a third line (transversal) intersects two other lines. These angles are on opposite sides of the transversal and are outside the other two lines.. A is a line that intersects two or more lines. 3. are pairs of angles formed when a third line (transversal) 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) intersects two other lines. These angles are on opposite sides of the transversal and are in between the other two lines. 5. are pairs of angles formed when a third line (transversal) 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 73

14 Lesson 10.3 Skills Practice page Problem Set Sketch an example of each. 1. Transversal. Alternate interior angles 3. Alternate exterior angles. Same-side interior angles 5. Same-side exterior angles 6. Corresponding angles 7 Chapter 10 Skills Practice

15 Lesson 10.3 Skills Practice page 3 Use the map to give an example of each type of relationship. Taylor Ave Monroe Dr Roosevelt Ave Polk Way Hoover Ave 1 Wilson Ave transversal Hoover Ave. is a transversal that intersects Monroe Dr. and Polk Way.. alternate interior angles 9. alternate exterior angles 10. same-side interior angles 11. same-side exterior angles 1. corresponding angles Chapter 10 Skills Practice 75

16 Lesson 10.3 Skills Practice page Complete each statement with congruent or supplementary. 13. The alternate interior angles formed when two parallel lines are intersected by a transversal are congruent. 1. 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 x x 76 Chapter 10 Skills Practice

17 Lesson 10.3 Skills Practice page x 0 x 75 1 Chapter 10 Skills Practice 77

18 Lesson 10.3 Skills Practice page 6 1. Solve for the value of x and y given that l 1 i l.. Solve for the value of x given that l 1 i l. 1 x x 55 y 7 Chapter 10 Skills Practice

19 Lesson 10. Skills Practice Parallel or Perpendicular? Slopes of Parallel and Perpendicular Lines Vocabulary Define each term in your own words. 1. Reciprocal. Negative reciprocal Problem Set Determine the slope of a line parallel to the given line represented by each equation. 1. y 5 6x 1 1 The slope of the line is 6, so the slope of a line parallel to it is 6.. y 5 3 x 5 3. y 5 5x. y x Chapter 10 Skills Practice 79

20 Lesson 10. Skills Practice page 5. 3x 1 y x 5y 5 0 Identify the slope of the line represented by each equation to determine which equations represent parallel lines. 7. a. y 5 x 5 b. y 5 7 x c. y 5 1 x slope 5 slope 5 slope 5 The equations (a) and (c) represent parallel lines.. a. y 5 6 3x b. y 5 3x c. y 5 3x a. 5y 5 0x 5 b. y 5 x 1 6 c. y x 730 Chapter 10 Skills Practice

21 Lesson 10. Skills Practice page a. y 5 x 16 b. y 5 1 x c. 3y 5 6x a. 3x 1 5y 5 60 b. 6x 1 10y 5 0 c. 15x 1 9y 5 1 Chapter 10 Skills Practice 731

22 Lesson 10. Skills Practice page 1. a. x 1 y 5 b. 3x 1 y 5 1 c. 0x 1 5y 5 10 Determine the negative reciprocal of each number Chapter 10 Skills Practice

23 Lesson 10. Skills Practice page 5 Determine the slope of a line perpendicular to the given line represented by each equation. 19. y 5 13x 1 0. y 5 5x 17 The slope of the line is 13, so the slope of a line perpendicular to it is y x 1. y x 3. 5x 1 6y x 3y 5 1 Chapter 10 Skills Practice 733

24 Lesson 10. Skills Practice page 6 Identify the slope of the line represented by each equation to determine which equations represent perpendicular lines. 5. a. y 5 3 x b. y 5 3 x 1 c. y 5 3 x 1 1 slope 5 3 slope 5 3 The equations (a) and (c) represent perpendicular lines. slope a. y 5 5x 3 b. y x c. y 5 5x a. 6y 5 x 1 1 b. y 5 3x 1 c. 9y 5 6x Chapter 10 Skills Practice

25 Lesson 10. Skills Practice page 7. a. 5y 5 5x 1 55 b. 5y 5 x 1 15 c. y 5 0x 9. a. 6x 1 y 5 0 b. 9x 3y 5 1 c. x 1 3y 5 15 Chapter 10 Skills Practice 735

26 Lesson 10. Skills Practice page 30. a. 3x 1 1y 5 7 b. 30x 1 5y 5 5 c. x 1 1y 5 Determine whether the lines described by the equations are parallel, perpendicular, or neither. 31. y 5 5x 1 y 5 1 5x slope 5 5 slope 5 5 The slopes are equal, so the lines are parallel. 3. y 5 15 x y 5 1 x y x 1 5 y 5 3x 736 Chapter 10 Skills Practice

27 Lesson 10. Skills Practice page x 1 1y 5 0x 1 5y x 1 y 5 x 1 3y 5 3 Chapter 10 Skills Practice 737

28 Lesson 10. Skills Practice page y 5 6x 1 0 1x 1 0y Chapter 10 Skills Practice

29 Lesson 10.5 Skills Practice 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 units to create line CD. Calculate the slope of each line to determine if the lines are parallel. y Line AB is parallel to line CD. C A D B x line AB: m 5 y y 1 x x line CD: m 5 y y 1 x x Chapter 10 Skills Practice 739

30 Lesson 10.5 Skills Practice page. Vertically translate line AB units to create line CD. Calculate the slope of each line to determine if the lines are parallel. y B A x 6 3. Horizontally translate line AB 5 units to create line CD. Calculate the slope of each line to determine if the lines are parallel. y 6 B A x 70 Chapter 10 Skills Practice

31 Lesson 10.5 Skills Practice page 3. Horizontally translate line AB 6 units to create line CD. Calculate the slope of each line to determine if the lines are parallel. y 6 B 6 6 x A 6 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 6 A 6 6 B 6 x Chapter 10 Skills Practice 71

32 Lesson 10.5 Skills Practice page 6. Horizontally translate line AB 3 units to create line CD. Calculate the slope of each line to determine if the lines are parallel. y 6 A 6 6 B x 6 Sketch the rotation for each line. 7. Use point A as the point of rotation and rotate line AB 90 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 6 C A B x line AB: m 5 y y 1 x x line AC: m 5 y y 1 x x Line AB is perpendicular to line AC because the slopes are negative reciprocals of each other. 7 Chapter 10 Skills Practice

33 Lesson 10.5 Skills Practice page 5. Use point B as the point of rotation and rotate line AB 90 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 6 B 6 A 6 x 6 9. Use point A as the point of rotation and rotate line AB 90 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 6 A 6 6 B 6 x Chapter 10 Skills Practice 73

34 Lesson 10.5 Skills Practice page Use point B as the point of rotation and rotate line AB 90 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 6 A 6 6 x B Use point A as the point of rotation and rotate line AB 90 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 B 6 A x 7 Chapter 10 Skills Practice

35 Lesson 10.5 Skills Practice page 7 1. Use point B as the point of rotation and rotate line AB 90 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 6 A 6 6 B x 6 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. y B 6 F A E 6 C 6 x G D 6 H slope of AB 5 5 slope of EF 5 5 AB i EF 5 slope of CD 5 5 slope of GH 5 CD i GH Chapter 10 Skills Practice 75

36 Lesson 10.5 Skills Practice page 1. y 6 A E F 6 B 6 x y 6 E F A B 6 6 x y F 6 B E A 6 6 x 6 76 Chapter 10 Skills Practice

37 Lesson 10.5 Skills Practice page A E y 6 F B 6 6 x 6 1. y 6 E A F 6 6 B x 6 Chapter 10 Skills Practice 77

38 7 Chapter 10 Skills Practice

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