parallel and perpendicular lines answer key

A(3, 4),y = x + 8 The points are: (-3, 7), (0, -2) Compare the above equation with Answer: c = 5 7 Click here for More Geometry Worksheets Then, according to the parallel line axiom, there is a different line than L2 that passes through the intersection point of L2 and L3 (point A in the drawing), which is parallel to L1. In Exercises 15 and 16, use the diagram to write a proof of the statement. Question 31. We know that, Answer: Question 12. y = x 6 -(1) So, b. m1 + m4 = 180 // Linear pair of angles are supplementary Question 33. x = c Perpendicular to $y=x$ and passing through $(7, 13)$. Proof: We can observe that x and 35 are the corresponding angles Compare the given equation with Answer: Question 32. Compare the given points with Hence, from the above, Answer: We know that, Write an inequality for the slope of a line perpendicular to l. Explain your reasoning. We can conclude that the distance between the meeting point and the subway is: 364.5 yards, Question 13. Question 30. So, Answer: Question 5. intersecting Answer: Explanation: Explain your reasoning. y = -x 12 (2) To be proficient in math, you need to analyze relationships mathematically to draw conclusions. So, So, Yes, there is enough information to prove m || n For parallel lines, x = $\frac{112}{8}$ It is given that the given angles are the alternate exterior angles We can conclude that 4 and 5 are the Vertical angles. a) Parallel to the given line: We can conclude that So, The given lines are: $\frac{5}{2}$x = 5 Slope of ST = $\frac{2}{-4}$ A(- 2, 3), y = $\frac{1}{2}$x + 1 If we try to find the slope of a perpendicular line by finding the opposite reciprocal, we run into a problem: $m_{}=\frac{1}{0}$, which is undefined. Question 42. We get, If you will see a tiger, then you go to the zoo-> False. (x1, y1), (x2, y2) Answer: We can observe that m2 and m3 Substitute P(-8, 0) in the above equation From the given figure, So, WRITING P(4, 0), x + 2y = 12 We can observe that To find the y-intercept of the equation that is perpendicular to the given equation, substitute the given point and find the value of c, Question 4. Furthermore, the rise and run between two perpendicular lines are interchanged. 2x = 3 We know that, (6, 22); y523 x1 4 13. b. Answer: Question 31. (E) The given figure is: y = $\frac{1}{6}$x 8 .And Why To write an equation that models part of a leaded glass window, as in Example 6 3-7 11 Slope and Parallel Lines Key Concepts Summary Slopes of Parallel Lines If two nonvertical lines are parallel, their slopes are equal. The coordinates of line d are: (-3, 0), and (0, -1) Similarly, in the letter E, the horizontal lines are parallel, while the single vertical line is perpendicular to all the three horizontal lines. c = -1 a. From the given figure, Use the steps in the construction to explain how you know that$\overline{C D}$ is the perpendicular bisector of $\overline{A B}$. 2 = 140 (By using the Vertical angles theorem) From the given coordinate plane, Negative reciprocal means, if m1 and m2 are negative reciprocals of each other, their product will be -1. Write the equation of the line that is perpendicular to the graph of 9y = 4x , and whose y-intercept is (0, 3). So, So, Answer: Question 48. We can conclude that 1 and 5 are the adjacent angles, Question 4. Parallel to $y=3$ and passing through $(2, 4)$. Linea and Line b are parallel lines Algebra 1 worksheet 36 parallel and perpendicular lines answer key. y = $\frac{1}{4}$x + b (1) y = $\frac{1}{2}$x + 8, Question 19. Answer: The given statement is: Compare the given equation with In Exercises 11 and 12, describe and correct the error in the statement about the diagram. y = $\frac{1}{2}$x + c $m\cdot m_{\perp}=-\frac{5}{8}\cdot\frac{8}{5}=-\frac{40}{40}=-1\quad\color{Cerulean}{\checkmark}$. Justify your answer. Slope of JK = $\frac{n 0}{0 0}$ Answer: Find an equation of the line representing the bike path. Answer: If the pairs of corresponding angles are, congruent, then the two parallel lines are. A coordinate plane has been superimposed on a diagram of the football field where 1 unit = 20 feet. Answer: Hence, Here is a quick review of the point/slope form of a line. Slope (m) = $\frac{y2 y1}{x2 x1}$ The Alternate Exterior Angles Theorem states that, when two parallel lines are cut by a transversal, the resulting alternate exterior angles are congruent An equation of the line representing Washington Boulevard is y = $\frac{2}{3}$x. The equation that is perpendicular to the given line equation is: So, So, x z and y z Answer: The opposite sides are parallel and the intersecting lines are perpendicular. (2, 4); m = $\frac{1}{2}$ d = 17.02 y 175 = $\frac{1}{3}$ (x -50) So, The coordinates of the meeting point are: (150. a. d = $\sqrt{(x2 x1) + (y2 y1)}$ The given equation is: So, To prove: l || k. Question 4. Hence, 1 (m2) = -3 The representation of the parallel lines in the coordinate plane is: Question 16. The slope of the parallel line that passes through (1, 5) is: 3 = 1 y = -x -(1) Question 1. Determine the slope of a line perpendicular to $3x7y=21$. What shape is formed by the intersections of the four lines? We can conclude that the number of points of intersection of coincident lines is: 0 or 1. The slope of the equation that is parallel t the given equation is: 3 So, y = -2x + $\frac{9}{2}$ (2) Answer: y = -x + c We can conclude that the pair of skew lines are: The perpendicular equation of y = 2x is: We know that, = $\frac{4}{-18}$ m2 = -2 The slope of the parallel line is 0 and the slope of the perpendicular line is undefined. The coordinates of the school = (400, 300) Slope of RS = 3, Slope of ST = $\frac{3 1}{1 5}$ $\frac{3}{2}$ . Perpendicular Transversal Theorem A carpenter is building a frame. Now, According to the Vertical Angles Theorem, the vertical angles are congruent Answer: Question 29. Draw $\overline{P Z}$, Question 8. The pair of lines that are different from the given pair of lines in Exploration 2 are: Answer: -x + 2y = 12 P(- 7, 0), Q(1, 8) REASONING y = -2x + c The given figure shows that angles 1 and 2 are Consecutive Interior angles We can conclude that the distance from the given point to the given line is: $\frac{4}{5}$. If we draw the line perpendicular to the given horizontal line, the result is a vertical line. Then use a compass and straightedge to construct the perpendicular bisector of $\overline{A B}$, Question 10. Converse: Question 25. We know that, Compare the given points with Hence, from the above, So, The slope of the parallel equations are the same y = $\frac{3}{2}$x 1 We know that, So, Hence, from the above, 2 and 3 Perpendicular lines are intersecting lines that always meet at an angle of 90. The slopes are equal fot the parallel lines Now, Which type of line segment requires less paint? So, Two lines are cut by a transversal. c = -3 c = 5 + 3 We know that, Possible answer: 1 and 3 b. The standard linear equation is: So, y = 3x + 2, (b) perpendicular to the line y = 3x 5. The given figure is: 1 and 3 are the vertical angles Answer: Slope (m) = $\frac{y2 y1}{x2 x1}$ The equation that is parallel to the given equation is: c = -4 + 3 m2 and m4 If the corresponding angles formed are congruent, then two lines l and m are cut by a transversal. Answer: The given equation is: Prove the Relationship: Points and Slopes This section consists of exercises related to slope of the line. We can conclude that the line that is perpendicular to $\overline{C D}$ is: $\overline{A D}$ and $\overline{C B}$, Question 6. = 4 We know that, Check out the following pages related to parallel and perpendicular lines. How do you know that n is parallel to m? The product of the slopes of the perpendicular lines is equal to -1 The given perpendicular line equations are: y = 4x 7 AC is not parallel to DF. So, = | 4 + $\frac{1}{2}$ | Parallel and Perpendicular Lines Maintaining Mathematical Proficiency Find the slope of the line. Example 2: State true or false using the properties of parallel and perpendicular lines. Identify all the linear pairs of angles. The Intersecting lines have a common point to intersect The equation for another line is: The parallel line equation that is parallel to the given equation is: So, Hence, Hence, from the given figure, So, lines intersect at 90. We know that, The given points are: Hence, from the above, 1 = 180 57 We know that, y = -7x + c 1 = 60 1 + 138 = 180 Prove $\overline{A B} \| \overline{C D}$ 2x + 72 = 180 We know that, The representation of the given point in the coordinate plane is: Question 54. Where, Work with a partner: The figure shows a right rectangular prism. The Converse of the Corresponding Angles Theorem says that if twolinesand a transversal formcongruentcorresponding angles, then thelinesare parallel. The given statement is: Question 18. For example, the letter H, in which the vertical lines are parallel and the horizontal line is perpendicular to both the vertical lines. Name two pairs of congruent angles when $\overline{A D}$ and $\overline{B C}$ are parallel? b is the y-intercept The representation of the parallel lines in the coordinate plane is: In Exercises 17 20. write an equation of the line passing through point P that is perpendicular to the given line. Question 3. The equation that is perpendicular to the given equation is: We know that, Answer: = 0 The distance between the given 2 parallel lines = | c1 c2 | Look at the diagram in Example 1. The equation that is parallel to the given equation is: The slope of perpendicular lines is: -1 If we see a few real-world examples, we can notice parallel lines in them, like the opposite sides of a notebook or a laptop, represent parallel lines, and the intersecting sides of a notebook represent perpendicular lines. x = 97 If the corresponding angles are congruent, then the lines cut by a transversal are parallel Also the two lines are horizontal e. m1 = ( 7 - 5 ) / ( -2 - (-2) ) m2 = ( 13 - 1 ) / ( 5 - 5 ) The two slopes are both undefined since the denominators in both m1 and m2 are equal to zero. So, So, Cops the diagram with the Transitive Property of Parallel Lines Theorem on page 141. 69 + 111 = 180 The postulates and theorems in this book represent Euclidean geometry. -x + 2y = 14 2x = 120 HOW DO YOU SEE IT? Step 2: Substitute the slope you found and the given point into the point-slope form of an equation for a line. answer choices y = -x + 4 y = x + 6 y = 3x - 5 y = 2x Question 6 300 seconds Q. Solved algebra 1 name writing equations of parallel and chegg com 3 lines in the coordinate plane ks ig kuta perpendicular to a given line through point you 5 elsinore high school horizontal vertical worksheets from equation ytic geometry practice khan academy common core infinite pdf study guide From the given figure, From the given figure, Answer/Step-by-step Explanation: To determine if segment AB and CD are parallel, perpendicular, or neither, calculate the slope of each. Identifying Parallel Lines Worksheets We can conclude that the vertical angles are: We can observe that the given lines are parallel lines Answer: Question 50. Perpendicular lines have slopes that are opposite reciprocals, so remember to find the reciprocal and change the sign. Perpendicular Postulate: Possible answer: 1 and 3 b. Answer: So, Is your friend correct? Answer: 11y = 77 During a game of pool. x y = -4 = $\frac{8}{8}$ (x + 14)= 147 From the Consecutive Exterior angles Converse, If r and s are the parallel lines, then p and q are the transversals. Fold the paper again so that point A coincides with point B. Crease the paper on that fold. So, Hence, Question 29. According to the Vertical Angles Theorem, the vertical angles are congruent d. AB||CD // Converse of the Corresponding Angles Theorem. 2m2 = -1 So, Classify the pairs of lines as parallel, intersecting, coincident, or skew. Answer: How would your m = 3 So, Answer: In Exercises 9 and 10, trace $\overline{A B}$. Answer: 3 + 8 = 180 So, Now, Answer: Question 44. The converse of the given statement is: Enter a statement or reason in each blank to complete the two-column proof. Where, Now, To find the value of c, When two lines are cut by a transversal, the pair ofangleson one side of the transversal and inside the two lines are called theconsecutive interior angles. So, by the _______ , g || h. In the proof in Example 4, if you use the third statement before the second statement. Slope of line 2 = $\frac{4 + 1}{8 2}$ We can observe that We can conclude that 2 and 7 are the Vertical angles, Question 5. Which point should you jump to in order to jump the shortest distance? If it is warm outside, then we will go to the park The given equation of the line is: a.) a. m5 + m4 = 180 //From the given statement The given point is: A (2, 0) x || y is proved by the Lines parallel to Transversal Theorem. The lines perpendicular to $\overline{Q R}$ are: $\overline{R M}$ and $\overline{Q L}$, Question 2. Hence, One answer is the line that is parallel to the reference line and passing through a given point. Question 11. The equation that is perpendicular to the given equation is: (13, 1) and (9, 4) So, Question 13. Prove m||n Answer: The given points are: The points are: (0, 5), and (2, 4) y = $\frac{77}{11}$ The slope of first line (m1) = $\frac{1}{2}$ We can conclude that there are not any parallel lines in the given figure, Question 15. We know that, Hence, Answer: Question 12. The construction of the walls in your home were created with some parallels. Find m2 and m3. Answer: Question 38. The product of the slopes of the perpendicular lines is equal to -1 y = 3x + c y = $\frac{1}{4}$x + 4, Question 24. (D) The conjectures about perpendicular lines are: So, The given figure is: Similarly, observe the intersecting lines in the letters L and T that have perpendicular lines in them. The product of the slopes of the perpendicular lines is equal to -1 The slopes of perpendicular lines are undefined and 0 respectively Write an equation of the line that passes through the given point and is we can conclude that the converse we obtained from the given statement is false, c. Alternate Exterior Angles Theorem (Theorem 3.3): If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent. Given a Pair of Lines Determine if the Lines are Parallel, Perpendicular, or Intersecting So, We can conclude that y = -2x + c Given Slopes of Two Lines Determine if the Lines are Parallel, Perpendicular, or Neither a. x = $\frac{153}{17}$ = $\frac{11}{9}$ Now, Answer: Question 14. Hence, From the given bars, We can conclude that the distance from line l to point X is: 6.32. y = $\frac{1}{2}$x 2 Proof of the Converse of the Consecutive Exterior angles Theorem: To find the coordinates of P, add slope to AP and PB So, 1 and 3 are the corresponding angles, e. a pair of congruent alternate interior angles From the given figure, The given point is: A (-3, 7) x 2y = 2 The lines that do not intersect to each other and are coplanar are called Parallel lines So, Question 3. So, Question 17. View Notes - 4.5 Equations of Parallel and Perpendicular Lines.pdf from BIO 187 at Beach High School. From the given figure, -5 2 = b Answer: So, The coordinates of the line of the second equation are: (1, 0), and (0, -2) Follows 1 Expert Answers 1 Parallel And Perpendicular Lines Math Algebra Middle School Math 02/16/20 Slopes of Parallel and Perpendicular Lines The map shows part of Denser, Colorado, Use the markings on the map. We can conclude that the lines x = 4 and y = 2 are perpendicular lines, Question 6. a) Parallel line equation: m is the slope The product of the slopes is -1 Is your friend correct? If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line = $\sqrt{31.36 + 7.84}$ So, The distance from the point (x, y) to the line ax + by + c = 0 is: Question 4. From the given figure, To find the value of c, The slope of PQ = $\frac{y2 y1}{x2 x1}$ The equation of a line is x + 2y = 10. We have to prove that m || n We know that, Corresponding Angles Theorem: So, The representation of the given pair of lines in the coordinate plane is: We can conclude that both converses are the same We can conclude that The given figure is: The Parallel lines are the lines that do not intersect with each other and present in the same plane $\frac{1}{2}$ . a. The Converse of Corresponding Angles Theorem: Hence, from the above, It is given that your school has a budget of $1,50,000 but we only need $1,20,512 A (-2, 2), and B (-3, -1) The distance from the point (x, y) to the line ax + by + c = 0 is: We will use Converse of Consecutive Exterior angles Theorem to prove m || n We know that, Hence, from the above, m2 = $\frac{1}{3}$ d = | ax + by + c| /$\sqrt{a + b}$ (1) = Eq. Answer: Hence, from the above, The given table is: We can conclude that the pair of parallel lines are: = $\frac{3 + 5}{3 + 5}$ y = 2x and y = 2x + 5 From the given figure, Question 22. c.) False, parallel lines do not intersect each other at all, only perpendicular lines intersect at 90. -9 = 3 (-1) + c 4x + 2y = 180(2) Name them. We know that, m1m2 = -1 Hence, 2x = 7 m = $\frac{0 2}{7 k}$ Answer: So, Parallel and perpendicular lines can be identified on the basis of the following properties: If the slope of two given lines is equal, they are considered to be parallel lines. Describe how you would find the distance from a point to a plane. So, 8 = 180 115 The given equation in the slope-intercept form is: line(s) PerPendicular to . The representation of the perpendicular lines in the coordinate plane is: In Exercises 21 24, find the distance from point A to the given line. x = $\frac{84}{7}$ y = 180 35 Answer: Slope of AB = $\frac{4}{6}$ Step 6: So, Q (2, 6), R (6, 4), S (5, 1), and T (1, 3) c = 2 + 2 y = x + c Answer: Now, You and your family are visiting some attractions while on vacation. We know that, So, Identify two pairs of perpendicular lines. So, The equation that is parallel to the given equation is: Answer: Given a||b, 2 3 $\frac{1}{3}$m2 = -1 2x y = 4 Now, Answer: Substitute the given point in eq. Sketch what the segments in the photo would look like if they were perpendicular to the crosswalk. c = $\frac{26}{3}$ This can be proven by following the below steps: We can observe that the given lines are perpendicular lines We get Begin your preparation right away and clear the exams with utmost confidence. We can conclude that In exercises 25-28. copy and complete the statement. x = 133 4.7 of 5 (20 votes) Fill PDF Online Download PDF. So, 2 and 3 are vertical angles Proof: The given figure is: So, 6x = 87 1 8, d. m6 + m ________ = 180 by the Consecutive Interior Angles Theorem (Thm. EG = $\sqrt{(5) + (5)}$ These worksheets will produce 10 problems per page. y = x 6 From the given figure, We know that, Alternate Interior Angles are a pair of angleson the inner side of each of those two lines but on opposite sides of the transversal. We can conclude that the argument of your friend that the answer is incorrect is not correct, Think of each segment in the figure as part of a line. In this case, the slope is $m_{}=\frac{1}{2}$ and the given point is $(8, 2)$. So, Determine whether the converse is true. The given point is: (-5, 2) m = 2 We know that, (B) Alternate Interior Angles Converse (Thm 3.6) = $\frac{2}{-6}$ C(5, 0) The Converse of the consecutive Interior angles Theorem states that if the consecutive interior angles on the same side of a transversal line intersecting two lines are supplementary, then the two lines are parallel. Now, Justify your conclusion. Explain. The slope of the line of the first equation is: Parallel to $x=2$ and passing through (7, 3)\). We can conclude that the values of x and y are: 9 and 14 respectively. The given figure is: m2 = 2 Answer: The given point is: (4, -5) Explain your reasoning. So, So, y = -2x + b (1) Answer: = -1 d = | 2x + y | / $\sqrt{5}$} Hence, from the above, So, Hence, b.) Answer: The equation that is perpendicular to the given line equation is: Write an equation of the line that passes through the given point and is parallel to the Get the best Homework key We can observe that From the given figure, The equation that is perpendicular to the given line equation is: 1 = 2 = 123, Question 11. The lines that have an angle of 90 with each other are called Perpendicular lines Fro the given figure, Answer: Question 2. So, Slope (m) = $\frac{y2 y1}{x2 x1}$ The distance wont be in negative value, According to the Perpendicular Transversal Theorem, We can conclude that = $\sqrt{(4 5) + (2 0)}$ From the given figure, 10x + 2y = 12 m a, n a, l b, and n b m1 m2 = -1 We know that, line(s) perpendicular to . Now, Compare the given equation with Substitute P (4, 0) in the above equation to find the value of c The representation of the Converse of the Consecutive Interior angles Theorem is: Question 2. What are Parallel and Perpendicular Lines? m1m2 = -1 By using the parallel lines property, y = $\frac{3}{2}$x 1 Slope (m) = $\frac{y2 y1}{x2 x1}$ By using the Corresponding angles Theorem, The given point is: A(3, 6) y = $\frac{5}{3}$x + $\frac{40}{3}$ 3 = 2 ( 0) + c We can observe that the given angles are corresponding angles (2) So, a. The slope of PQ = $\frac{y2 y1}{x2 x1}$ Solution: We need to know the properties of parallel and perpendicular lines to identify them. The conjecture about $\overline{A B}$ and $\overline{c D}$ is: transv. y = 3x 5 The completed table of the nature of the given pair of lines is: Work with a partner: In the figure, two parallel lines are intersected by a third line called a transversal. We can observe that 48 and y are the consecutive interior angles and y and (5x 17) are the corresponding angles To find the distance from point X to $\overline{W Z}$, Slope of line 2 = $\frac{4 6}{11 2}$ The Coincident lines are the lines that lie on one another and in the same plane 2x = -6 Solution to Q6: No. So, your friend claims to be able to make the shot Shown in the diagram by hitting the cue ball so that m1 = 25. From the given figure, The given parallel line equations are: a.) Explain your reasoning. We know that, = 5.70 could you still prove the theorem? The given figure is: y = 2x + c Two lines are cut by a transversal. Now, X (3, 3), Y (2, -1.5) We can conclude that the value of XZ is: 7.07, Find the length of $\overline{X Y}$ Let the congruent angle be P c = $\frac{16}{3}$ 2: identify a parallel or perpendicular equation to a given graph or equation. y = $\frac{1}{3}$x 4 Compare the given points with (0, 9); m = $\frac{2}{3}$ Now, The slope of perpendicular lines is: -1 $\frac{6-(-4)}{8-3}$ Question 20. a is perpendicular to d and b isperpendicular to c, Question 22. Hence, from the above, Answer: Question 2. Hence, from the above, HOW DO YOU SEE IT? line(s) perpendicular to EG = $\sqrt{50}$ Prove: l || m Hence, from the above, Angles Theorem (Theorem 3.3) alike? MAKING AN ARGUMENT So, The given equation is: So, 2 = $\frac{1}{4}$ (8) + c We know that, Hence, We know that, Compare the given equation with x = 5 In this case, the negative reciprocal of -4 is 1/4 and vice versa. XY = $\sqrt{(6) + (2)}$ So, The given coordinates are: A (-2, 1), and B (4, 5) In Exercises 19 and 20. describe and correct the error in the conditional statement about lines. If m1 = 58, then what is m2? Answer: Answer: The perpendicular lines have the product of slopes equal to -1 = $\frac{6 0}{0 + 2}$ c = 7 9 Slope (m) = $\frac{y2 y1}{x2 x1}$ In a plane, if a line is perpendicular to one of two parallellines, then it is perpendicular to the other line also. When two lines are cut by a transversal, the pair of angles on one side of the transversal and inside the two lines are called the Consecutive interior angles Hence, from the given figure, a. Alternate Interior angles theorem: The given point is: A (3, -1) The portion of the diagram that you used to answer Exercise 26 on page 130 is: Question 2. The standard form of the equation is: MODELING WITH MATHEMATICS It is given that We know that, Intersecting lines can intersect at any . Now, ATTENDING TO PRECISION Approximately how far is the gazebo from the nature trail? Now, (- 5, 2), y = 2x 3 In Exercises 13 and 14, prove the theorem. (2) = $\sqrt{(3 / 2) + (3 / 2)}$ y = $\frac{1}{5}$x + c y = -3 (0) 2 Often you have to perform additional steps to determine the slope. consecutive interior Hence, It is given that 4 5. = $1,20,512 The equation of the line that is perpendicular to the given line equation is: Now, The given pair of lines are: The lengths of the line segments are equal i.e., AO = OB and CO = OD. Think of each segment in the figure as part of a line. We know that, What point on the graph represents your school? $\frac{1}{2}$x + 1 = -2x 1 A _________ line segment AB is a segment that represents moving from point A to point B. This contradicts what was given,that angles 1 and 2 are congruent. A Linear pair is a pair of adjacent angles formed when two lines intersect In Example 4, the given theorem is Alternate interior angle theorem Step 1: Find the slope $m$. The slope of the given line is: m = -3 Although parallel and perpendicular lines are the two basic and most commonly used lines in geometry, they are quite different from each other. $\frac{8-(-3)}{7-(-2)}$ Write the equation of the line that is perpendicular to the graph of 53x y = , and From the given figure, MATHEMATICAL CONNECTIONS Slope of the line (m) = $\frac{y2 y1}{x2 x1}$ Explain your reasoning. Parallel and Perpendicular Lines From the given slopes of the lines, identify whether the two lines are parallel, perpendicular, or neither. We can conclude that Explain. Find both answers. Substitute (-5, 2) in the given equation The slopes of the parallel lines are the same x and 61 are the vertical angles alternate exterior The given point is: (-1, 5) We know that, So, FSE = ESR x = 9. If the line cut by a transversal is parallel, then the corresponding angles are congruent If a || b and b || c, then a || c Use the numbers and symbols to create the equation of a line in slope-intercept form 8 = -2 (-3) + b Determine the slope of parallel lines and perpendicular lines. = 8.48 y = $\frac{1}{3}$x + $\frac{16}{3}$, Question 5. 2 = 180 123 From the given figure, The vertical angles are congruent i.e., the angle measures of the vertical angles are equal

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