Draw a diagram of at least two lines cut by at least one transversal. So, Answer: We have to divide AB into 10 parts Question 1. Answer: The given point is: (-3, 8) In Exercises 11 and 12. prove the theorem. Now, A (-2, 2), and B (-3, -1) d = \(\sqrt{(13 9) + (1 + 4)}\) We can conclude that the top step is also parallel to the ground since they do not intersect each other at any point, Question 6. m1 m2 = -1 Answer: Two lines, a and b, are perpendicular to line c. Line d is parallel to line c. The distance between lines a and b is x meters. y = -2x + 8 c = 3 In the diagram, how many angles must be given to determine whether j || k? The lines that do not intersect and are not parallel and are not coplanar are Skew lines (2) Hence, from the given figure, Hence, from the above, We know that, = \(\frac{-6}{-2}\) (13, 1) and (9, 4) For example, the opposite sides of a square and a rectangle have parallel lines in them, and the adjacent lines in the same shapes are perpendicular lines. Hence, from the above, Which lines are parallel to ? Hence, from the above, We know that, Hence, from the above, The Alternate Interior Angles Theorem states that, when two parallel lines are cut by a transversal, the resultingalternate interior anglesare congruent Classify the lines as parallel, perpendicular, coincident, or non-perpendicular intersecting lines. b is the y-intercept The equation that is perpendicular to the given line equation is: Question 25. 68 + (2x + 4) = 180 Justify your answers. = -3 We can conclude that quadrilateral JKLM is a square. By comparing the given pair of lines with The representation of the Converse of the Exterior angles Theorem is: d. Consecutive Interior Angles Theorem (Theorem 3.4): If two parallel lines are cut by a transversal. 6 + 4 = 180, Question 9. Compare the given points with 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 The given equation is: The given equation is: A (x1, y1), and B (x2, y2) Question 13. We can conclude that the converse we obtained from the given statement is true When we compare the given equation with the obtained equation, THINK AND DISCUSS 1. The points are: (-9, -3), (-3, -9) So, Explain. If two parallel lines are cut by a transversal, then the pairs of Corresponding angles are congruent. Substitute A (-\(\frac{1}{4}\), 5) in the above equation to find the value of c x = 60 a = 1, and b = -1 m2 = 1 The y-intercept is: -8, Writing Equations of Parallel and Perpendicular Lines, Work with a partner: Write an equation of the line that is parallel or perpendicular to the given line and passes through the given point. 1 + 2 = 180 2 = 180 3 The given point is: C (5, 0) Answer: The given figure is: So, These Parallel and Perpendicular Lines Worksheets will give the student a pair of equations for lines and ask them to determine if the lines are parallel, perpendicular, or intersecting. Now, Answer: PDF 4-4 Study Guide and Intervention You and your family are visiting some attractions while on vacation. Homework 2 - State whether the given pair are parallel, perpendicular, or intersecting. We get Answer: a. We know that, We know that, (2x + 20) = 3x The equation of a line is: (D) A, B, and C are noncollinear. You can select different variables to customize these Parallel and Perpendicular Lines Worksheets for your needs. Hence, The given line equation is: Perpendicular to \(x=\frac{1}{5}\) and passing through \((5, 3)\). c = -9 3 The given point is: A (-\(\frac{1}{4}\), 5) What is the distance that the two of you walk together? From the given figure, CONSTRUCTING VIABLE ARGUMENTS For a pair of lines to be non-perpendicular, the product of the slopes i.e., the product of the slope of the first line and the slope of the second line will not be equal to -1 Using the same compass selling, draw an arc with center B on each side \(\overline{A B}\). From the above, Now, The flow proof for the Converse of Alternate exterior angles Theorem is: By using the linear pair theorem, A(- 2, 4), B(6, 1); 3 to 2 From the given figure, If two lines are horizontal, then they are parallel d = 32 Answer: Question 26. Question 23. Now, From the given coordinate plane, Name the line(s) through point F that appear skew to . Answer: Question 40. We know that, Hence, from the above, According to Corresponding Angles Theorem, Compare the given points with y = \(\frac{1}{2}\)x + c The Intersecting lines have a common point to intersect Hence, In this case, the negative reciprocal of -4 is 1/4 and vice versa. The given figure is: Once the equation is already in the slope intercept form, you can immediately identify the slope. So, Geometry parallel and perpendicular lines answer key P(0, 0), y = 9x 1 d = \(\frac{4}{5}\) The parallel line equation that is parallel to the given equation is: Using a compass setting greater than half of AB, draw two arcs using A and B as centers Given m1 = 105, find m4, m5, and m8. A (x1, y1), B (x2, y2) The general steps for finding the equation of a line are outlined in the following example. what Given and Prove statements would you use? The equation that is perpendicular to the given line equation is: = \(\frac{-3}{-4}\) Let the given points are: From the given figure, The Alternate Interior angles are congruent Write an equation for a line parallel to y = 1/3x - 3 through (4, 4) Q. Question 12. If you were to construct a rectangle, So, Now, So, This is why we took care to restrict the definition to two nonvertical lines. By using the corresponding angles theorem, = \(\frac{5}{6}\) Work with a partner: Write the equations of the parallel or perpendicular lines. Now, So, Compare the given points with (x1, y1), and (x2, y2) Now, Remember that horizontal lines are perpendicular to vertical lines. (4.3.1) - Parallel and Perpendicular Lines - Lumen Learning = \(\frac{-3}{4}\) Substitute A (2, 0) in the above equation to find the value of c Question 42. The lines that have the same slope and different y-intercepts are Parallel lines We know that, y = \(\frac{1}{6}\)x 8 Hence, from the above, We can observe that the figure is in the form of a rectangle So, We can conclude that the number of points of intersection of parallel lines is: 0, a. Now, y = -7x 2. Now, m = \(\frac{-30}{15}\) Consecutive Interior Angles Converse (Theorem 3.8) c = 8 \(\frac{3}{5}\) x = \(\frac{40}{8}\) We use this and the point \((\frac{7}{2}, 1)\) in point-slope form. So, Answer: Hence, from the above, Hence, from the above figure, The conjecture about \(\overline{A O}\) and \(\overline{O B}\) is: Exercise \(\PageIndex{3}\) Parallel and Perpendicular Lines. We know that, Maintaining Mathematical Proficiency Name a pair of parallel lines. So, Now, We know that, y = x 6 -(1) For example, if the equation of two lines is given as, y = 4x + 3 and y = 4x - 5, we can see that their slope is equal (4). The parallel lines have the same slope but have different y-intercepts and do not intersect (11y + 19) = 96 m1 m2 = -1 The given point is: (4, -5) The slope of the given line is: m = \(\frac{1}{2}\) We can conclude that the given pair of lines are non-perpendicular lines, work with a partner: Write the number of points of intersection of each pair of coplanar lines. Now, The given figure is: m1 = \(\frac{1}{2}\), b1 = 1 y = -2x + c The lines perpendicular to \(\overline{E F}\) are: \(\overline{F B}\) and \(\overline{F G}\), Question 3. Using the properties of parallel and perpendicular lines, we can answer the given questions. y = mx + c 3. Parallel Lines - Lines that move in their specific direction without ever intersecting or meeting each other at a point are known as the parallel lines. y = 3x 6, Question 20. x = 29.8 and y = 132, Question 7. To make the top of the step where 1 is present to be parallel to the floor, the angles must be Alternate Interior angles From the given figure, The given figure is: EG = \(\sqrt{(5) + (5)}\) The distance from the point (x, y) to the line ax + by + c = 0 is: Compare the given equation with So, Apply slope formula, find whether the lines are parallel or perpendicular. A(- 2, 3), y = \(\frac{1}{2}\)x + 1 We know that, Hence, Example 2: State true or false using the properties of parallel and perpendicular lines. Horizontal and vertical lines are perpendicular to each other. We can conclude that the value of x is: 133, Question 11. 5y = 3x 6 Cellular phones use bars like the ones shown to indicate how much signal strength a phone receives from the nearest service tower. In Exercises 13-18. decide whether there is enough information to prove that m || n. If so, state the theorem you would use. = \(\frac{-1}{3}\) Answer: Is your classmate correct? Compare the given equation with We can conclude that the line parallel to \(\overline{N Q}\) is: \(\overline{M P}\), b. Question 3. So, Finding Parallel and Perpendicular Lines - mathsisfun.com The given figure is: Angles Theorem (Theorem 3.3) alike? XY = \(\sqrt{(6) + (2)}\) Question: What is the difference between perpendicular and parallel? So, b.) Hence, Compare the given coordinates with (x1, y1), and (x2, y2) 8 = 65. c = 0 Algebra 1 Writing Equations of Parallel and Perpendicular Lines 1) through: (2, 2), parallel to y = x + 4. If both pairs of opposite sides of a quadrilateral are parallel, then it is a parallelogram We can observe that the product of the slopes are -1 and the y-intercepts are different Linea and Line b are parallel lines If the slope of one is the negative reciprocal of the other, then they are perpendicular. Now, We have to find the point of intersection Save my name, email, and website in this browser for the next time I comment. The given figure is: In the same way, when we observe the floor from any step, According to the Perpendicular Transversal Theorem, So, Alternate Exterior Angles Theorem (Thm. Hence, from the above figure, 3 = 68 and 8 = (2x + 4) y = -x + 4 -(1) 1 + 2 = 180 Explain. Answer: So, In Exercises 43 and 44, find a value for k based on the given description. Now, So, y = \(\frac{2}{3}\)x + 9, Question 10. Answer: So, The given equation is: The equation of a line is: Answer: We know that, \(\begin{aligned} y-y_{1}&=m(x-x_{1}) \\ y-1&=-\frac{1}{7}\left(x-\frac{7}{2} \right) \\ y-1&=-\frac{1}{7}x+\frac{1}{2} \\ y-1\color{Cerulean}{+1}&=-\frac{1}{7}x+\frac{1}{2}\color{Cerulean}{+1} \\ y&=-\frac{1}{7}x+\frac{1}{2}+\color{Cerulean}{\frac{2}{2}} \\ y&=-\frac{1}{7}x+\frac{3}{2} \end{aligned}\). We want to prove L1 and L2 are parallel and we will prove this by using Proof of Contradiction Substitute (4, -5) in the above equation We can say that w and v are parallel lines by Perpendicular Transversal Theorem Explain why the tallest bar is parallel to the shortest bar. From the given figure, Hence, from the above, Answer: Answer: Where, In this form, we see that perpendicular lines have slopes that are negative reciprocals, or opposite reciprocals. The equation of the line that is perpendicular to the given line equation is: y = \(\frac{1}{3}\)x + \(\frac{16}{3}\), Question 5. The slope of the given line is: m = -3 Now, It is important to have a geometric understanding of this question. Describe and correct the error in writing an equation of the line that passes through the point (3, 4) and is parallel to the line y = 2x + 1. a) Parallel to the given line: Slope of QR = \(\frac{-2}{4}\) Example: Write an equation in slope-intercept form for the line that passes through (-4, 2) and is perpendicular to the graph of 2x - 3y = 9. We know that, In Example 2, can you use the Perpendicular Postulate to show that is not perpendicular to ? y = 3x + 9 When we compare the given equation with the obtained equation, Answer: Find the distance from point X to Find the slope of the line perpendicular to \(15x+5y=20\). The slope of the line of the first equation is: We know that, m || n is true only when x and 73 are the consecutive interior angles according to the Converse of Consecutive Interior angles Theorem Answer: Question 1. So, So, Examine the given road map to identify parallel and perpendicular streets. Difference Between Parallel and Perpendicular Lines, Equations of Parallel and Perpendicular Lines, Parallel and Perpendicular Lines Worksheets. A(3, 4), y = x -x = x 3 Answer: We can conclude that the value of x when p || q is: 54, b. These worksheets will produce 6 problems per page. So, We can observe that the given lines are parallel lines Are the markings on the diagram enough to conclude that any lines are parallel? Often you will be asked to find the equation of a line given some geometric relationshipfor instance, whether the line is parallel or perpendicular to another line. Hence, from the above, Substitute A (0, 3) in the above equation We know that, y = -2x + c If you multiply theslopesof twoperpendicular lines in the plane, you get 1 i.e., the slopes of perpendicular lines are opposite reciprocals. The equation that is perpendicular to the given equation is: From the given figure, Some examples follow. The given point is: P (4, 0) Question 4. The Parallel and Perpendicular Lines Worksheets are randomly created and will never repeat so you have an endless supply of quality Parallel and Perpendicular Lines Worksheets to use in the classroom or at home. We know that, XZ = \(\sqrt{(x2 x1) + (y2 y1)}\) For perpediclar lines, So, y = mx + c Hence, We can observe that the product of the slopes are -1 and the y-intercepts are different 0 = \(\frac{5}{3}\) ( -8) + c The given point is: (3, 4) y = 3x + c We can observe that Hence, from the coordinate plane, A(- 6, 5), y = \(\frac{1}{2}\)x 7 -3 = -4 + c Hence, from the above, Here the given line has slope \(m=\frac{1}{2}\), and the slope of a line parallel is \(m_{}=\frac{1}{2}\). The given equation is: These Parallel and Perpendicular Lines Worksheets will ask the student to find the equation of a perpendicular line passing through a given equation and point. According to Contradiction, These worksheets will produce 6 problems per page. Alternate Exterior angle Theorem: The slopes are equal fot the parallel lines Let A and B be two points on line m. y = \(\frac{1}{2}\)x 4, Question 22. a. m1=m3 So, a) Parallel to the given line: We know that, 1 + 18 = b Answer: Question 14. y = \(\frac{1}{7}\)x + 4 Answer: 11 and 13 It is given that m || n as shown. Parallel and Perpendicular Lines - Definition, Properties, Examples 1 (m2) = -3 Answer: \(\frac{3}{2}\) . Writing Equations Of Parallel And Perpendicular Lines Answer Key Kuta (C) are perpendicular The given point is: (-1, 5) MAKING AN ARGUMENT So, Substitute A (-9, -3) in the above equation to find the value of c FSE = ESR A(- \(\frac{1}{4}\), 5), x + 2y = 14 We can say that A (-3, -2), and B (1, -2) If two straight lines lie in the same plane, and if they never intersect each other, they are called parallel lines. We can conclude that the distance from point A to the given line is: 5.70, Question 5. x and 61 are the vertical angles A (x1, y1), and B (x2, y2) Where, 9. From the above, We know that, The given statement is: 1 8 Answer: Observe the horizontal lines in E and Z and the vertical lines in H, M and N to notice the parallel lines. Answer: (y + 7) = (3y 17) Question 25. -4 1 = b The theorem we can use to prove that m || n is: Alternate Exterior angles Converse theorem. d = 17.02 Question 43. Answer: The distance from point C to AB is the distance between point C and A i.e., AC You are trying to cross a stream from point A. Answer: Question 28. So, We can conclude that the consecutive interior angles of BCG are: FCA and BCA. From the figure, 1 = 4 The equation that is perpendicular to the given line equation is: The representation of the given pair of lines in the coordinate plane is: The plane parallel to plane ADE is: Plane GCB. The given figure is: PDF CHAPTER Solutions Key 3 Parallel and Perpendicular Lines The slope that is perpendicular to the given line is: 4 = 105, To find 5: From the given figure, If you will see a tiger, then you go to the zoo-> False. Art and Culture: Abstract Art: Lines, Rays, and Angles - Saskia Lacey 2017-09-01 Students will develop their geometry skills as they study the geometric shapes of modern art and read about the . 4x + 2y = 180(2) Answer: Slope (m) = \(\frac{y2 y1}{x2 x1}\) So, So, Find the values of x and y. The line parallel to \(\overline{E F}\) is: \(\overline{D H}\), Question 2. So, Write an equation for a line perpendicular to y = -5x + 3 through (-5, -4) If you go to the zoo, then you will see a tiger Construct a square of side length AB a. b.) The lines that have the slopes product -1 and different y-intercepts are Perpendicular lines x 6 = -x 12 Justify your answer. The angles that are opposite to each other when 2 lines cross are called Vertical angles Draw \(\overline{A B}\), as shown. y = \(\frac{1}{3}\)x + \(\frac{475}{3}\) We know that, We know that, Now, From the given figure, To be proficient in math, you need to analyze relationships mathematically to draw conclusions. Since the given line is in slope-intercept form, we can see that its slope is \(m=5\). Slope of AB = \(\frac{-4 2}{5 + 3}\) y = \(\frac{137}{5}\) The equation for another line is: Hence, from the above, Answer: So, We know that, Answer: x + x = -12 + 6 Answer: From the given figure, Which line(s) or plane(s) appear to fit the description? 1 2 3 4 5 6 7 8 So, The equation for another line is: Now, (x1, y1), (x2, y2) We can conclude that the value of x is: 60, Question 6. y = -2x 2, f. 2x = 108 3x 2x = 20 a. = 5.70 Answer: x y + 4 = 0 Given: m5 + m4 = 180 Hence, Parallel and Perpendicular Lines Worksheets - Math Worksheets Land The given point is: (-8, -5) If the corresponding angles are congruent, then the lines cut by a transversal are parallel 4x = 24 We can conclude that the distance that the two of the friends walk together is: 255 yards. Work with a partner: The figure shows a right rectangular prism. \(\frac{5}{2}\)x = 2 The equation of line p is: So, We can observe that there are 2 perpendicular lines From the figure, Parallel & perpendicular lines from equation Writing equations of perpendicular lines Writing equations of perpendicular lines (example 2) Write equations of parallel & perpendicular lines Proof: parallel lines have the same slope Proof: perpendicular lines have opposite reciprocal slopes Analytic geometry FAQ Math > High school geometry > y = mx + b For example, the letter H, in which the vertical lines are parallel and the horizontal line is perpendicular to both the vertical lines. 6 (2y) 6(3) = 180 42 We know that, The two pairs of parallel lines so that each pair is in a different plane are: q and p; k and m, b. The converse of the Alternate Interior angles Theorem: CRITICAL THINKING 6x = 140 53 Answer: In a plane, if a line is perpendicular to one of the two parallel lines, then it is perpendicular to the other line also Prove m||n Hence, from the above, From the given figure, Answer: These worksheets will produce 6 problems per page. Eq. m1m2 = -1 Solution to Q6: No. Parallel to \(x+y=4\) and passing through \((9, 7)\). are parallel, or are the same line. y = 0.66 feet y = x + 4 Solving the concepts from the Big Ideas Math Book Geometry Ch 3 Parallel and Perpendicular Lines Answers on a regular basis boosts the problem-solving ability in you. Question 1. Name them. Compare the given points with (x1, y1), (x2, y2) 1 = 180 138 y = -x -(1) Hence, from the above, We get Alternate Exterior Angles Theorem: The equation that is perpendicular to the given line equation is: Unit 3 (Parallel & Perpendicular Lines) In this unit, you will: Identify parallel and perpendicular lines Identify angle relationships formed by a transversal Solve for missing angles using angle relationships Prove lines are parallel using converse postulate and theorems Determine the slope of parallel and perpendicular lines Write and graph If the corresponding angles formed are congruent, then two lines l and m are cut by a transversal. d = \(\sqrt{(4) + (5)}\) In Exercises 9 and 10, use a compass and straightedge to construct a line through point P that is parallel to line m. Question 10. = 3 y = \(\frac{1}{3}\)x \(\frac{8}{3}\). Answer: Geometrically, we note that if a line has a positive slope, then any perpendicular line will have a negative slope. answer choices y = -x + 4 y = x + 6 y = 3x - 5 y = 2x Question 6 300 seconds Q. Hence, from the above figure, Given: 1 and 3 are supplementary The points are: (2, -1), (\(\frac{7}{2}\), \(\frac{1}{2}\)) A(6, 1), y = 2x + 8 We have to divide AB into 5 parts The slope of the line of the first equation is: Unit 3 Test Parallel And Perpendicular Lines Answer Key Pdf - Fill Compare the given equation with x = 20 Which of the following is true when are skew? VOCABULARY The vertical angles are: 1 and 3; 2 and 4 We know that, Hence, Answer: Compare the given equation with It is given that your classmate claims that no two nonvertical parallel lines can have the same y-intercept Answer: = \(\frac{-4}{-2}\) Answer: The equation of line q is: Hence, from the above, The coordinates of x are the same. We know that, Algebra 1 worksheet 36 parallel and perpendicular lines answer key. Step 1: Answer: They are not parallel because they are intersecting each other. X (3, 3), Y (2, -1.5) We can conclude that the equation of the line that is perpendicular bisector is: So, x = 4 and y = 2 Line 1: (- 3, 1), (- 7, 2) m1m2 = -1 Hence, from the above, Answer: m = \(\frac{1}{4}\) To be proficient in math, you need to understand and use stated assumptions, definitions, and previously established results. A(- 3, 2), B(5, 4); 2 to 6 Answer: So, Answer: We know that, such as , are perpendicular to the plane containing the floor of the treehouse. If the slope of two given lines are negative reciprocals of each other, they are identified as perpendicular lines. The coordinates of line 2 are: (2, -1), (8, 4) The third intersecting line can intersect at the same point that the two lines have intersected as shown below: Make a conjecture about how to find the coordinates of a point that lies beyond point B along \(\vec{A}\)B. From the given figure, Answer: y = mx + b c = 8 Answer: In Exercises 17-22, determine which lines, if any, must be parallel. The equation for another parallel line is: The point of intersection = (-1, \(\frac{13}{2}\)) Answer: Question 40. 2x and 2y are the alternate exterior angles The line that passes through point F that appear skew to \(\overline{E H}\) is: \(\overline{F C}\), Question 2. AB = 4 units So, Hence, from the given figure, The parallel lines have the same slopes Answer: Two nonvertical lines in the same plane, with slopes \(m_{1}\) and \(m_{2}\), are perpendicular if the product of their slopes is \(1: m1m2=1\). 2 = 180 1 Line 1: (10, 5), (- 8, 9) Prove: AB || CD Slope of line 2 = \(\frac{4 6}{11 2}\) Answer: The points of intersection of intersecting lines: Draw a line segment CD by joining the arcs above and below AB Question 7. If m1 = 58, then what is m2? = \(\frac{-3}{-1}\) Explain your reasoning. Answer: Answer: It is given that m || n The lines that have the slopes product -1 and different y-intercepts are Perpendicular lines Hence. y = \(\frac{5}{3}\)x + \(\frac{40}{3}\) transv. 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. Geometry chapter 3 parallel and perpendicular lines answer key - Math 3y = x 50 + 525 By comparing the slopes, Your friend claims that because you can find the distance from a point to a line, you should be able to find the distance between any two lines. 2-4 Additional Practice Parallel And Perpendicular Lines Answer Key November 7, 2022 admin 2-4 Extra Observe Parallel And Perpendicular Strains Reply Key. For the intersection point of y = 2x, ABSTRACT REASONING The given point is: (-5, 2) Compare the given points with According to the Perpendicular Transversal Theorem, We can observe that The parallel lines have the same slope 1 and 3 are the vertical angles So, The equation that is perpendicular to the given line equation is: Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. We can conclude that the distance from point A to the given line is: 2.12, Question 26. x = \(\frac{112}{8}\) Answer: 4.6: Parallel and Perpendicular Lines - Mathematics LibreTexts x = \(\frac{180}{2}\) Answer: m = 2 (-1) (m2) = -1 b.) We can conclude that the distance between the given 2 points is: 6.40. Answer: AP : PB = 3 : 7 The lines skew to \(\overline{Q R}\) are: \(\overline{J N}\), \(\overline{J K}\), \(\overline{K L}\), and \(\overline{L M}\), Question 4. The given figure is: Hence, from the above, Answer: Two lines are cut by a transversal. Describe how you would find the distance from a point to a plane. Answer: a. m5 + m4 = 180 //From the given statement We can conclude that your friend is not correct. Simply click on the below available and learn the respective topics in no time. So, alternate interior, alternate exterior, or consecutive interior angles. Answer: 8 = -2 (-3) + b We know that, x = 90 From the given figure, y = -7x + c = \(\frac{8}{8}\) c = \(\frac{37}{5}\) They both consist of straight lines. Your classmate decided that based on the diagram. Hence, from the above, Answer: 5y = 137 So, k = 5 The diagram that represents the figure that it can not be proven that any lines are parallel is: b.) The points are: (-2, 3), (\(\frac{4}{5}\), \(\frac{13}{5}\)) Explain your reasoning. The slopes of the parallel lines are the same True, the opposite sides of a rectangle are parallel lines. (2x + 15) = 135 b = -7 From the given figure, We know that, Find the equation of the line passing through \((8, 2)\) and perpendicular to \(6x+3y=1\). What are the coordinates of the midpoint of the line segment joining the two houses? = (\(\frac{-2}{2}\), \(\frac{-2}{2}\)) The product of the slopes of the perpendicular lines is equal to -1 According to the Consecutive Interior Angles Theorem, the sum of the consecutive interior angles is 180 Hence, from the above, x = 54 Slope (m) = \(\frac{y2 y1}{x2 x1}\) 2x y = 4 = \(\frac{6 + 4}{8 3}\) Unit 3 Parallel And Perpendicular Lines Homework 4 Answer Key The theorems involving parallel lines and transversals that the converse is true are: From the given figure, Now, We know that, In the equation form of a line y = mx +b lines that are parallel will have the same value for m. Perpendicular lines will have an m value that is the negative reciprocal of the . Let's expand 2 (x 5) and then rearrange: y 4 = 2x 10. So, Hence, from the above, So, Proof of the Converse of the Consecutive Exterior angles Theorem: y = mx + c y1 = y2 = y3 (C) Alternate Exterior Angles Converse (Thm 3.7) alternate interior The given figure is: = \(\sqrt{(6) + (6)}\) Prove: l || m Eq. y = 144 Use a graphing calculator to verify your answer. Hence, Hence, from the above, The representation of the Converse of the Consecutive Interior angles Theorem is: Question 2. The equation of a line is: Hence, from the above, Question 5. 8x 4x = 24 We know that, 2 6, c. 1 ________ by the Alternate Exterior Angles Theorem (Thm. The slopes of perpendicular lines are undefined and 0 respectively Answer: Question 26. Describe and correct the error in determining whether the lines are parallel. So, The intersection point of y = 2x is: (2, 4) Explain your reasoning. If two lines are intersected by a third line, is the third line necessarily a transversal? Substitute the given point in eq. So, It is given that According to the Converse of the Corresponding Angles Theorem, m || n is true only when the corresponding angles are congruent Answer: y = \(\frac{1}{2}\)x + c Now, The standard linear equation is: y = x \(\frac{28}{5}\) Answer: The standard linear equation is: Is it possible for consecutive interior angles to be congruent? P = (3 + (\(\frac{3}{10}\) 3), 7 + (\(\frac{3}{10}\) 2)) Question 13. We know that, We can conclude that Hence, from the above, By using the vertical Angles Theorem, We know that, c = 6 The given figure is: Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. We can conclude that the given pair of lines are perpendicular lines, Question 2.