Lesson 10.1 Skills Practice

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1 Lesson 0. Skills Practice Name_Date 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. Parallel lines are lines that lie in the same plane and do not intersect.. Intersecting lines are lines in a plane that cross or intersect each other. 3. Coincidental lines are lines that have equivalent linear equations and overlap at every point when they are graphed.. Perpendicular lines are lines that intersect at a right angle. 5. Skew lines are lines that do not lie in the same plane.. Coplanar lines 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... perpendicular lines, intersecting lines, coplanar lines parallel lines, coplanar lines Chapter 0 Skills Practice 7

2 Lesson 0. Skills Practice page 3.. coincidental lines, coplanar lines coplanar lines, intersecting lines 5.. intersecting lines, coplanar lines skew lines Sketch an example of each relationship. Answers will vary. 7. parallel lines. coplanar lines 7 Chapter 0 Skills Practice

3 Lesson 0. Skills Practice page 3 Name_Date 9. intersecting lines 0. perpendicular lines. coincidental lines. skew lines Choose the description from the box that best describes each sketch. Case : 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. 3.. Case Case Chapter 0 Skills Practice 73

4 Lesson 0. Skills Practice page 5.. Case Case Case Case 3 7 Chapter 0 Skills Practice

5 Lesson 0. Skills Practice page 5 Name_Date 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 9. intersecting lines Answers will vary. 0. perpendicular lines Answers will vary. Ivy Lane and Plum Street Magnolia Drive and Cherry Street. parallel lines Answers will vary.. skew lines None. All streets are in the same plane. Cherry Street and Chestnut Street 3. coincidental lines North Daisy Lane and South Daisy Lane. coplanar lines Answers will vary. All streets are in the same plane. Chapter 0 Skills Practice 75

6 7 Chapter 0 Skills Practice

7 Lesson 0. Skills Practice Name Date When Lines Come Together Angle Relationships Formed by Two Intersecting Lines Vocabulary Match each definition to its corresponding term.. Two adjacent angles that form a straight line b. linear pair of angles a. supplementary angles. Two angles whose sum is 0 degrees a. supplementary angles b. linear pair of angles Problem Set Sketch an example of each relationship. Answers will vary.. congruent figures. congruent angles adjacent angles. vertical angles 0 0 Chapter 0 Skills Practice 77

8 Lesson 0. Skills Practice page 5. linear pair 0 0. supplementary angles 35 5 Use the map to give an example of each relationship. Answers will vary. Willow Drive Main Street Franklin Drive 3 Fifth Ave Sixth Ave 7. congruent angles 3 and 9. supplementary angles 9 and 0. vertical angles and 5 0. linear pair and. adjacent angles 7 and. vertical angles and 7 7 Chapter 0 Skills Practice

9 Lesson 0. Skills Practice page 3 Name Date Complete each sketch. Answers may vary. 3. Draw adjacent to /.. Draw / such that it forms a vertical angle with /. 5. Draw / such that it supplements / and does not share a common side Draw / adjacent to /. Chapter 0 Skills Practice 79

10 Lesson 0. Skills Practice page 7. Draw / such that it forms a vertical angle with /.. Draw / such that it forms a linear pair with /. Determine each unknown angle measure. 9. If / and / form a linear pair and m/ 5, what is m/? m m 5 0 x 5 0 x 5 3 m Chapter 0 Skills Practice

11 Lesson 0. Skills Practice page 5 Name Date 0. If / and / are supplementary angles and m/ 5 0, what is m/? m m x 5 0 x 5 79 m If / and / form a linear pair and m/ is one-fifth m/, what is the measure of each angle? m m x x 5 0.x 5 0 x 5 50 and 0.x 5 0.(50) 5 30 m 5 50 and m If / and / are supplementary angles and m/ is 0 less than m/, what is the measure of each angle? m m 5 0 (x 0) x 5 0 x 5 0 x 5 0 and x m 5 0 and m 5 0 Chapter 0 Skills Practice 7

12 Lesson 0. Skills Practice page 3. If / and / form a linear pair and m/ is three times m/, what is the measure of each angle? m m 5 0 3x x 5 0 x 5 0 x 5 5 and 3x 5 3(5) 5 35 m 5 5 and m If / and / are supplementary angles and m/ is more than m/, what is the measure of each angle? m m 5 0 (x ) x 5 0 x 5 x 5 and x m 5 and m Chapter 0 Skills Practice

13 Lesson 0.3 Skills Practice Name Date 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. Alternate exterior angles 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 transversal is a line that intersects two or more lines. 3. Same-side exterior angles 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.. Alternate interior angles 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. Same-side interior angles 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 0 Skills Practice 73

14 Lesson 0.3 Skills Practice page Problem Set Sketch an example of each. Answers will vary.. Transversal. Alternate interior angles 3. Alternate exterior angles. Same-side interior angles 5. Same-side exterior angles. Corresponding angles 7 Chapter 0 Skills Practice

15 Lesson 0.3 Skills Practice page 3 Name Date Use the map to give an example of each type of relationship. Answers will vary. Taylor Ave Monroe Dr Roosevelt Ave Polk Way Hoover Ave Wilson Ave transversal Hoover Ave. is a transversal that intersects Monroe Dr. and Polk Way.. alternate interior angles and 5 9. alternate exterior angles and 0. same-side interior angles and 5. same-side exterior angles and 3. corresponding angles and Chapter 0 Skills Practice 75

16 Lesson 0.3 Skills Practice page Complete each statement with congruent or supplementary. 3. The alternate interior angles formed when two parallel lines are intersected by a transversal are congruent.. The same-side interior angles formed when two parallel lines are intersected by a transversal are supplementary. 5. The alternate exterior angles formed when two parallel lines are intersected by a transversal are congruent.. The same-side exterior angles formed when two parallel lines are intersected by a transversal are supplementary. Determine the measure of all the angles in each x x 3 x x 5 0 5x 5 0 x 5 3 x 5 7 Chapter 0 Skills Practice

17 Lesson 0.3 Skills Practice page 5 Name Date x x x 0 x 5 0 x x 5 00 x 5 00 x Chapter 0 Skills Practice 77

18 Lesson 0.3 Skills Practice page. Solve for the value of x and y given that l l.. Solve for the value of x given that l l. x x y 90 y 5 0 y 5 90 x 5 0 x 5 7 Chapter 0 Skills Practice

19 Lesson 0. Skills Practice Name Date Parallel or Perpendicular? Slopes of Parallel and Perpendicular Lines Vocabulary Define each term in your own words.. Reciprocal When the product of two numbers is, the numbers are reciprocals of one another.. Negative reciprocal When the product of two numbers is, the numbers are negative reciprocals of one another. Problem Set Determine the slope of a line parallel to the given line represented by each equation.. y 5 x The slope of the line is, so the slope of a line parallel to it is.. y 5 3 x 5 The slope of the line is, so the 3 slope of a line parallel to it is y 5 5x The slope of the line is 5, so the slope of a line parallel to it is 5.. y 5 x The slope of the line is, so the slope of a line parallel to it is. Chapter 0 Skills Practice 79

20 Lesson 0. Skills Practice page 5. 3x y 5 3x y 5. 5x 5y 5 0 5x 5y 5 0 y 5 3x y 5 3 x The slope of the line is 3, so the slope of a line parallel to it is 3. 5y 5 0 5x y 5 3x The slope of the line is 3, so the slope of a line parallel to it is 3. 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 x slope 5 slope 5 slope 5 The equations (a) and (c) represent parallel lines.. a. y 5 3x b. y 5 3x c. y 5 3x 0 slope 5 3 slope 5 3 slope 5 3 The equations (a) and (b) represent parallel lines. 9. a. 5y 5 0x 5 b. y 5 x c. y 5 3 x 5y 5 0x 5 y 5 x y 5 3 x y 5 x 9 y 5 x 3 y 5 x slope 5 slope 5 slope 5 The equations (a) and (c) represent parallel lines. 730 Chapter 0 Skills Practice

21 Lesson 0. Skills Practice page 3 Name Date 0. a. y 5 x b. y 5 x c. 3y 5 x y 5 x y 5 x 3y 5 x y 5 x y 5 x y 5 x slope 5 slope 5 slope 5 The equations (b) and (c) represent parallel lines.. a. 3x 5y 5 0 b. x 0y 5 0 c. 5x 9y 5 3x 5y 5 0 x 0y 5 0 5x 9y 5 5y 5 3x 0 0y 5 x 0 9y 5 5x y 5 3 slope x y 5 0 x y x 5 y x y x The equations (a) and (b) represent parallel lines. slope slope Chapter 0 Skills Practice 73

22 Lesson 0. Skills Practice page. a. x y 5 b. 3x y 5 c. 0x 5y 5 0 x y 5 3x y 5 0x 5y 5 0 y 5 x y 5 3x 5y 5 0x 0 y 5 x 3 y 5 x 3 y 5 x slope 5 slope 5 slope 5 The equations (b) and (c) represent parallel lines. Determine the negative reciprocal of each number Chapter 0 Skills Practice

23 Lesson 0. Skills Practice page 5 Name Date Determine the slope of a line perpendicular to the given line represented by each equation. 9. y 5 3x The slope of the line is 3, so the slope of a line perpendicular to it is y 5 5x 7 The slope of the line is 5, so the slope of a line perpendicular to it is 5.. y 5 x The slope of the line is, so the slope of a line perpendicular to it is.. y x The slope of the line is, so the 3 slope of a line perpendicular to it is x y 5 3 5x y 5 3. x 3y 5 x 3y 5 y 5 5x 3 y 5 5 x The slope of the line is 5, so the slope of a line perpendicular to it is 5. 3y 5 x y 5 3 x 7 The slope of the line is, so the 3 slope of a line perpendicular to it is 3. Chapter 0 Skills Practice 733

24 Lesson 0. Skills Practice page 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 c. y 5 3 x slope 5 3 slope 5 3 slope 5 3 The equations (a) and (c) represent perpendicular lines.. a. y 5 5x 3 b. y 5 x 5 c. y 5 5x 3 slope 5 5 slope 5 5 slope 5 5 The equations (a) and (b) represent perpendicular lines. 7. a. y 5 x b. y 5 3x c. 9y 5 x 9 y 5 x y 5 3x 9y 5 x 9 y 5 x y 5 3 x y 5 9 x y 5 x slope y 5 3 x slope 5 3 slope 5 3 The equations (b) and (c) represent perpendicular lines. 73 Chapter 0 Skills Practice

25 Lesson 0. Skills Practice page 7 Name Date. a. 5y 5 5x 55 b. 5y 5 x 5 c. y 5 0x 5y 5 5x 55 5y 5 x 5 y 5 0x y 5 5x y 5 x 3 5 y 5 5x slope 5 5 slope 5 5 slope 5 5 The equations (a) and (b) represent perpendicular lines. 9. a. x y 5 0 b. 9x 3y 5 c. x 3y 5 5 x y 5 0 9x 3y 5 x 3y 5 5 y 5 x 0 3y 5 9x 3y 5 x 5 y 5 3x 0 y 5 3x y 5 3 x 5 slope 5 3 slope 5 3 slope 5 3 The equations (a) and (c) represent perpendicular lines. Chapter 0 Skills Practice 735

26 Lesson 0. Skills Practice page 30. a. 3x y 5 7 b. 30x 5y 5 5 c. x y 5 3x y x 5y 5 5 x y 5 y 5 3x 7 5y 5 30x 5 y 5 x y 5 3 x y 5 x 5 y 5 x y 5 x slope 5 y 5 x slope 5 slope 5 The equations (b) and (c) represent perpendicular lines. Determine whether the lines described by the equations are parallel, perpendicular, or neither. 3. y 5 5x y 5 5x slope 5 5 slope 5 5 The slopes are equal, so the lines are parallel. 3. y 5 5 x y 5 x 7 slope 5 slope 5 The product of the slopes is, so the lines are perpendicular. 33. y 5 x 5 3 y 5 3x slope 5 3 slope 5 3 The product of the slopes is not, and the slopes are not equal, so the lines are not parallel or perpendicular. 73 Chapter 0 Skills Practice

27 Lesson 0. Skills Practice page 9 Name Date 3. 3x y 5 0x 5y 5 0 3x y 5 0x 5y 5 0 y 5 3x 5y 5 0x 0 y 5 3 x y 5 x y 5 x slope 5 slope 5 The product of the slopes is, so the lines are perpendicular x y 5 x 3y 5 3 3x y 5 x 3y 5 3 y 5 3x 3y 5 x 3 y 5 3 slope 5 3 x y 5 3 x slope 5 3 The product of the slopes is not, and the slopes are not equal, so the lines are neither parallel nor perpendicular. Chapter 0 Skills Practice 737

28 Lesson 0. Skills Practice page y 5 x 0 x 0y 5 0 0y 5 x 0 x 0y 5 0 y 5 x 0 0y 5 x 0 3 y 5 x 5 y 5 0 x 3 slope 5 5 y x 3 slope 5 5 The slopes are equal, so the lines are parallel. 73 Chapter 0 Skills Practice

29 Lesson 0.5 Skills Practice Name Date Up, Down, and All Around Line Transformations Vocabulary Write a definition for the term in your own words.. Triangle Sum Theorem The Triangle Sum Theorem states that the sum of the measures of the three interior angles of a triangle is equal to 0. Problem Set Sketch the translation for each line.. 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 x x _ line CD: m 5 y y x x Chapter 0 Skills Practice 739

30 Lesson 0.5 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. A y D C Line AB is parallel to line CD. B x line AB: m 5 _ y y x x () line CD: m 5 _ y y x x 5 0 (3) 3 () Horizontally translate line AB 5 units to create line CD. Calculate the slope of each line to determine if the lines are parallel. D y A C Line AB is parallel to line CD. B x line AB: m 5 _ y y x x 5 () (3) line CD: m 5 _ y y x x _ 5 () 3 () Chapter 0 Skills Practice

31 Lesson 0.5 Skills Practice page 3 Name Date. Horizontally translate line AB units to create line CD. Calculate the slope of each line to determine if the lines are parallel. y A Line AB is parallel to line CD. B C D x line AB: m 5 _ y y x x 5 (5) () 5 3 line CD: m 5 _ y y x x 5 (5) Vertically translate line AB 7 units to create line CD. Calculate the slope of each line to determine if the lines are parallel. C A y B D x line AB: m 5 _ y y x x 5 (3) line CD: m 5 _ y y x x 5 3 (3) Line AB is parallel to line CD. Chapter 0 Skills Practice 7

32 Lesson 0.5 Skills Practice page. Horizontally translate line AB 3 units to create line CD. Calculate the slope of each line to determine if the lines are parallel. C A y D Line AB is parallel to line CD. B x line AB: m 5 _ y y x x 5 () 5 5 line CD: m 5 _ y y x x _ 5 () 5 5 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 C A B x line AB: m 5 _ y y x x line AC: m 5 _ y y x x Line AB is perpendicular to line AC because the slopes are negative reciprocals of each other. 7 Chapter 0 Skills Practice

33 Lesson 0.5 Skills Practice page 5 Name Date. 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 C A B x line AB: m 5 _ y y x x _ line BC: m 5 y y x x 5 3 () 5 Line AB is perpendicular to line BC because the slopes are negative reciprocals of each other. 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. A y B C x line AB: m 5 _ y y x x 5 3 () 5 5 _ line AC: m 5 y y x x 5 0 () 5 5 Line AB is perpendicular to line AC because the slopes are negative reciprocals of each other. Chapter 0 Skills Practice 73

34 Lesson 0.5 Skills Practice page 0. 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. A y C B x line AB: m 5 _ y y x x _ 5 3 () _ 5 5 line BC: m 5 y y x x _ () Line AB is perpendicular to line BC because the slopes are negative reciprocals of each other.. 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. A y B C x line AB: m 5 _ y y x x _ 5 () 5 3 _ line AC: m 5 y y x x 5 0 () 5 3 Line AB is perpendicular to line AC because the slopes are negative reciprocals of each other. 7 Chapter 0 Skills Practice

35 Lesson 0.5 Skills Practice page 7 Name Date. 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 B C A x line AB: m 5 _ y y x x _ _ 5 line BC: m 5 y y x x _ 3 (7) 5 5 () 5 Line AB is perpendicular to line BC because the slopes are negative reciprocals of each other. 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. 3. y A C G D H E B F x slope of AB 5 5 slope of EF 5 5 AB EF 5 slope of CD 5 _ 5 slope of GH 5 _ CD GH Chapter 0 Skills Practice 75

36 Lesson 0.5 Skills Practice page. y E A F B C D G H x slope of AB 5 slope of EF 5 AB EF slope of CD 5 _ slope of GH 5 _ CD GH 5. y E F A B x C G D H slope of AB 5 slope of EF 5 AB EF slope of CD 5 _ slope of GH 5 _ CD GH. y F B E A D H C G x slope of AB 5 slope of EF 5 AB EF slope of CD 5 _ slope of GH 5 _ CD GH 7 Chapter 0 Skills Practice

37 Lesson 0.5 Skills Practice page 9 Name Date 7. y E A F B H x D G C slope of AB slope of EF AB EF slope of CD _ slope of GH _ CD GH. y E A C F B G D H x slope of AB 5 5 slope of EF 5 5 AB EF slope of CD 5 5 _ slope of GH 5 5 _ CD GH Chapter 0 Skills Practice 77

38 7 Chapter 0 Skills Practice

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