parallel and perpendicular lines answer key

= 1 A(- 3, 2), B(5, 4); 2 to 6 The given points are: Hence, from the above, y = 3x 6, Question 11. The slope of vertical line (m) = \(\frac{y2 y1}{x2 x1}\) We know that, m2 = \(\frac{1}{2}\) WRITING Given: k || l, t k Answer: Slope of QR = \(\frac{4 6}{6 2}\) For a square, Perpendicular Transversal Theorem A carpenter is building a frame. m1 m2 = -1 (E) Notice that the slope is the same as the given line, but the \(y\)-intercept is different. Answer: The given pair of lines are: The coordinates of line 2 are: (2, -4), (11, -6) This can be proven by following the below steps: Answer: Therefore, these lines can be identified as perpendicular lines. Question 15. = 2.12 The given figure is: Question 1. MAKING AN ARGUMENT Substitute (2, -2) in the above equation Answer: Question 24. Question 21. Answer: Question 40. x + 2y = 2 The slope of the equation that is perpendicular to the given equation is: \(\frac{1}{m}\) Answer: We can observe that the figure is in the form of a rectangle Write an equation of the line that passes through the given point and has the given slope. x = 29.8 and y = 132, Question 7. Find the perpendicular line of y = 2x and find the intersection point of the two lines Parallel, Perpendicular and Intersecting Lines Worksheets According to the Converse of the Corresponding Angles Theorem, m || n is true only when the corresponding angles are congruent We can conclude that in order to jump the shortest distance, you have to jump to point C from point A. The given figure is: Answer: Answer: Answer: Use a graphing calculator to verify your answers. The given figure is: From the given figure, Now, 1 = 4 c = -4 + 3 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 . y = 2x + c So, 4.6: Parallel and Perpendicular Lines - Mathematics LibreTexts b. m1 + m4 = 180 // Linear pair of angles are supplementary From the given coordinate plane, Are the numbered streets parallel to one another? We can observe that the slopes are the same and the y-intercepts are different x = 5 The given point is: P (3, 8) We can conclude that the line that is perpendicular to \(\overline{C D}\) is: \(\overline{A D}\) and \(\overline{C B}\), Question 6. We can conclude that m || n by using the Corresponding Angles Theorem, Question 14. MODELING WITH MATHEMATICS WHICH ONE did DOESNT BELONG? Answer: x = 14.5 Write an equation of a line parallel to y = x + 3 through (5, 3) Q. Hence, from the above, Compare the given points with (x1, y1), and (x2, y2) \(\frac{6-(-4)}{8-3}\) -x x = -3 4 From the given diagram, Answer: m1=m3 P || L1 Explain. We can also observe that w and z is not both to x and y What does it mean when two lines are parallel, intersecting, coincident, or skew? c. m5=m1 // (1), (2), transitive property of equality Unit 3 parallel and perpendicular lines homework 5 answer key Answer: 72 + (7x + 24) = 180 (By using the Consecutive interior angles theory) Hence, from the above, Hence, from the above, = \(\frac{3 + 5}{3 + 5}\) From the given figure, (7x + 24) = 180 72 1 4. Possible answer: plane FJH 26. plane BCD 2a. Slope of TQ = 3 Find both answers. Answer: Question 18. = \(\frac{325 175}{500 50}\) So, Explain. We can conclude that 2x = \(\frac{1}{2}\)x + 5 x = \(\frac{18}{2}\) Hence, Hence, from the above figure, We have to find 4, 5, and 8 The given figure is: We can conclude that 1 2. x = 54 Question 22. y = -2x + b (1) We know that, Answer: (2) Explain your reasoning. are parallel, or are the same line. Answer: 9 and x- Answer: 2 and y Answer: x +15 and Answer: x +10 2 x -6 and 2x + 3y Answer: 6) y and 3x+y=- Answer: Answer: 14 and y = 5 6 The product of the slopes of the perpendicular lines is equal to -1 From the given figure, So, We know that, Hence, By using the dynamic geometry, From the given figure, m1m2 = -1 The given equation is: The corresponding angles are: and 5; 4 and 8, b. alternate interior angles m = \(\frac{1}{2}\) Answer: The given figure is: Examples of perpendicular lines: the letter L, the joining walls of a room. P = (4, 4.5) a=30, and b=60 If Adam Ct. is perpendicular to Bertha Dr. and Charles St., what must be true? Explain why the top rung is parallel to the bottom rung. The slope of the line that is aprallle to the given line equation is: Which line(s) or plane(s) appear to fit the description? We know that, Chapter 3 Parallel and Perpendicular Lines Key. c = -13 MAKING AN ARGUMENT Explain your reasoning. Name them. Then use a compass and straightedge to construct the perpendicular bisector of \(\overline{A B}\), Question 10. So, The parallel line equation that is parallel to the given equation is: So, Now, Now, 3 = 180 133 To find the value of c, Possible answer: plane FJH plane BCD 2a. You are designing a box like the one shown. y = 7 We know that, So, (2x + 2) = (x + 56) We can observe that 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 We know that, Explain your reasoning. We can observe that So, So, The lines that do not have any intersection points are called Parallel lines So, d = \(\sqrt{(x2 x1) + (y2 y1)}\) 5 7 Draw the portion of the diagram that you used to answer Exercise 26 on page 130. We have to divide AB into 5 parts Proof: What are the coordinates of the midpoint of the line segment joining the two houses? In Exercises 19 and 20. describe and correct the error in the conditional statement about lines. (D) Consecutive Interior Angles Converse (Thm 3.8) y = \(\frac{1}{6}\)x 8 Label its intersection with \(\overline{A B}\) as O. Using Y as the center and retaining the same compass setting, draw an arc that intersects with the first The two lines are Intersecting when they intersect each other and are coplanar We know that, By using the vertical Angles Theorem, 2x = 7 For the intersection point, Slope of the line (m) = \(\frac{y2 y1}{x2 x1}\) A coordinate plane has been superimposed on a diagram of the football field where 1 unit = 20 feet. m2 = \(\frac{2}{3}\) c = -3 y = -2x + c y = -3x + 19, Question 5. The slope of the given line is: m = -2 a. We know that, 6-3 Write Equations of Parallel and Perpendicular Lines Worksheet. Perpendicular to \(y=2x+9\) and passing through \((3, 1)\). The equation that is parallel to the given equation is: According to the Alternate Interior Angles theorem, the alternate interior angles are congruent c.) False, parallel lines do not intersect each other at all, only perpendicular lines intersect at 90. Explain. Question 5. Answer: -1 = \(\frac{1}{3}\) (3) + c d = | ax + by + c| /\(\sqrt{a + b}\) The pair of angles on one side of the transversal and inside the two lines are called the Consecutive interior angles. The equation of the line along with y-intercept is: x = \(\frac{7}{2}\) c = 5 \(\frac{1}{2}\) From Exploration 2, So, The equation that is perpendicular to the given line equation is: y = -3x + c Solving Equations Involving Parallel and Perpendicular Lines www.BeaconLC.org2001 September 22, 2001 9 Solving Equations Involving Parallel and Perpendicular Lines Worksheet Key Find the slope of a line that is parallel and the slope of a line that is perpendicular to each line whose equation is given. The equation of the perpendicular line that passes through (1, 5) is: How would your x = n The given rectangular prism of Exploration 2 is: In Exploration 1, explain how you would prove any of the theorems that you found to be true. 2 = 0 + c So, The distance between the two parallel lines is: Consider the following two lines: Both lines have a slope \(m=\frac{3}{4}\) and thus are parallel. So, Proof of the Converse of the Consecutive Interior angles Theorem: From the given figure, Since, The resultant diagram is: = \(\frac{2}{-6}\) We can conclude that the given pair of lines are perpendicular lines, Question 2. Substitute (0, -2) in the above equation We can conclude that 11 and 13 are the Consecutive interior angles, Question 18. We can observe that 141 and 39 are the consecutive interior angles (a) parallel to and We can observe that when r || s, So, The equation that is perpendicular to the given equation is: From the given figure, The letter A has a set of perpendicular lines. Answer: Question 38. Line 1: (10, 5), (- 8, 9) Slope of AB = \(\frac{4 3}{8 1}\) The given figure is: The representation of the parallel lines in the coordinate plane is: Question 16. Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines So, 69 + 111 = 180 If you even interchange the second and third statements, you could still prove the theorem as the second line before interchange is not necessary These lines can be identified as parallel lines. We can conclude that option D) is correct because parallel and perpendicular lines have to be lie in the same plane, Question 8. Now, The equation of the line that is perpendicular to the given line equation is: We know that, then the slope of a perpendicular line is the opposite reciprocal: The mathematical notation \(m_{}\) reads \(m\) perpendicular. We can verify that two slopes produce perpendicular lines if their product is \(1\). The equation that is parallel to the given equation is: Sketch what the segments in the photo would look like if they were perpendicular to the crosswalk. We can conclude that the distance from point A to the given line is: 2.12, Question 26. Where, The slope of the equation that is parallel t the given equation is: \(\frac{1}{3}\) Hence, from the above, So, Substitute the given point in eq. We know that, We know that, = \(\frac{2}{9}\) Answer: Hence, from the above, -x + 4 = x 3 Now, 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. Compare the given coordinates with (x1, y1), and (x2, y2) You decide to meet at the intersection of lines q and p. Each unit in the coordinate plane corresponds to 50 yards. 4. For parallel lines, Select the angle that makes the statement true. Perpendicular lines are lines in the same plane that intersect at right angles (\(90\) degrees). The given figure is: x = -1 If the slope of AB and CD are the same value, then they are parallel. To be proficient in math, you need to make conjectures and build a logical progression of statements to explore the truth of your conjectures. From the given figure, We know that, We can conclude that your friend is not correct. y = x + 4 We can conclude that Hence, from the above, Hence, from the above, 42 + 6 (2y 3) = 180 Hence, from the above, Hence, from the above, Make a conjecture about what the solution(s) can tell you about whether the lines intersect. We can conclude that 1 = 2 = 3 = 4 = 5 = 6 = 7 = 8 = 80, Question 1. The representation of the Converse of the Consecutive Interior angles Theorem is: Question 2. Hence, from the above, P(- 8, 0), 3x 5y = 6 5 = -2 (-\(\frac{1}{4}\)) + c Answer: Identify the slope and the y-intercept of the line. Which point should you jump to in order to jump the shortest distance? From the given figure, Geometry Worksheets | Parallel and Perpendicular Lines Worksheets We know that, c = 3 y = \(\frac{1}{3}\)x + c We can observe that the product of the slopes are -1 and the y-intercepts are different x and 61 are the vertical angles The point of intersection = (\(\frac{4}{5}\), \(\frac{13}{5}\)) Answer: 42 and 6(2y 3) are the consecutive interior angles Answer: y = \(\frac{1}{2}\)x + c 8 = \(\frac{1}{5}\) (3) + c The coordinates of the midpoint of the line segment joining the two houses = (150, 250) Slope of line 2 = \(\frac{4 6}{11 2}\) The representation of the given pair of lines in the coordinate plane is: So, 8 = 65. Question 47. A line is a circle on the sphere whose diameter is equal to the diameter of the sphere. So, We can conclude that We know that, The equation of the line that is parallel to the line that represents the train tracks is: From the given figure, Slope of LM = \(\frac{0 n}{n n}\) Answer: The given points are A (-1, 2), and B (3, -1) Compare the given points with A (x1, y1), B (x2, y2) m = Substitute A (-1, 2), and B (3, -1) in the formula. Substitute (0, 2) in the above equation Substitute (1, -2) in the above equation a. We can conclude that the converse we obtained from the given statement is true Question 42. The length of the field = | 20 340 | 1 = 32 y = -x, Question 30. So, We can conclude that the line parallel to \(\overline{N Q}\) is: \(\overline{M P}\), b. So, We can conclude that the length of the field is: 320 feet, b. The given lines are perpendicular lines So, The theorem we can use to prove that m || n is: Alternate Exterior angles Converse theorem. y = \(\frac{2}{3}\) COMPLETE THE SENTENCE Answer: 68 + (2x + 4) = 180 XY = 4.60 REASONING We know that, 3.4). To find the value of c, Answer: The slope of one line is the negative reciprocal of the other line. The two pairs of perpendicular lines are l and n, c. Identify two pairs of skew line 2 = 41 Answer: Question 4. Hence, The given figure is: -2 \(\frac{2}{3}\) = c We can conclude that The given figure is: Write an equation for a line parallel to y = 1/3x - 3 through (4, 4) Q. Alternate Interior angles theorem: The line that is perpendicular to the given equation is: Answer: So, To find the coordinates of P, add slope to AP and PB y = 3x 5 We can conclude that the number of points of intersection of parallel lines is: 0, a. Answer: The given figure is: consecutive interior Now, The given figure is: d = \(\sqrt{41}\) -x x = -3 Each unit in the coordinate plane corresponds to 50 yards. x = 9. The given point is: A(3, 6) y = -2x + c (8x + 6) = 118 (By using the Vertical Angles theorem) We know that, The diagram shows lines formed on a tennis court. The slopes of the parallel lines are the same Determine the slope of a line perpendicular to \(3x7y=21\). Question 22. y = mx + b y = mx + c y = -2x 1 (2) The given points are: The converse of the given statement is: The slope of first line (m1) = \(\frac{1}{2}\) Slope of AB = \(\frac{2}{3}\) PROVING A THEOREM d = | 2x + y | / \(\sqrt{2 + (1)}\) 3 + 133 = 180 (By using the Consecutive Interior angles theorem) y = -x + 1. 2x + 4y = 4 We can observe that The slope of the parallel equations are the same y = 4x + 9, Question 7. Hence, from the above, So, = \(\sqrt{(3 / 2) + (3 / 2)}\) Geometrically, we see that the line \(y=4x1\), shown dashed below, passes through \((1, 5)\) and is perpendicular to the given line. Now, Using P as the center and any radius, draw arcs intersecting m and label those intersections as X and Y. 1 = 2 The lines skew to \(\overline{E F}\) are: \(\overline{C D}\), \(\overline{C G}\), and \(\overline{A E}\), Question 4. You are looking : parallel and perpendicular lines maze answer key pdf Contents 1. Answer: y = \(\frac{1}{2}\)x + 5 Examples of parallel lines: Railway tracks, opposite sides of a whiteboard. The given point is: A (-\(\frac{1}{4}\), 5) We have to divide AB into 5 parts So, We can conclude that b is perpendicular to c. Question 1. The given points are: Use the numbers and symbols to create the equation of a line in slope-intercept form It is given that We know that, x = \(\frac{69}{3}\) Describe the point that divides the directed line segment YX so that the ratio of YP Lo PX is 5 to 3. Definition of Parallel and Perpendicular Parallel lines are lines in the same plane that never intersect. If not, what other information is needed? y = \(\frac{1}{3}\)x + c FSE = ESR We can observe that the slopes of the opposite sides are equal i.e., the opposite sides are parallel c = 8 2 = 180 123 = 1.67 The given figure is: When we observe the ladder, Now, (-3, 7), and (8, -6) -4 1 = b (2) to get the values of x and y When we compare the given equation with the obtained equation, 2 and 7 are vertical angles Given: 1 2 b. Alternate Exterior angles Theorem y = \(\frac{1}{2}\)x + c Slope of the line (m) = \(\frac{-2 + 2}{3 + 1}\) Perpendicular and Parallel - Math is Fun From the figure, We can conclude that the claim of your classmate is correct. From the given figure, y = mx + c y = -x -(1) Question 18. y = 2x + 12 Now, By using the linear pair theorem, Draw a line segment of any length and name that line segment as AB The Converse of the alternate exterior angles Theorem: We can conclude that It is given that, So, Vertical Angles Theoremstates thatvertical angles,anglesthat are opposite each other and formed by two intersecting straight lines, are congruent Classify the pairs of lines as parallel, intersecting, coincident, or skew. Now, Consider the 2 lines L1 and L2 intersected by a transversal line L3 creating 2 corresponding angles 1 and 2 which are congruent PDF 4-4 Study Guide and Intervention The slope of the perpendicular line that passes through (1, 5) is: We get So, 3. We can conclude that the equation of the line that is parallel to the line representing railway tracks is: Now, Perpendicular to \(y3=0\) and passing through \((6, 12)\). d = 364.5 yards x = 40 So, c = 3 4 = \(\frac{8}{8}\) Answer: Question 14. Hence, The equation of the line that is parallel to the given equation is: When two lines are crossed by another line (which is called the Transversal), theanglesin matching corners are calledcorresponding angles. PROOF Write the equation of the line that is perpendicular to the graph of 53x y = , and The equation of a line is: The given equation is: In Exercises 11 and 12. find m1, m2, and m3. So, \(\begin{array}{cc}{\color{Cerulean}{Point}}&{\color{Cerulean}{Slope}}\\{(6,-1)}&{m_{\parallel}=\frac{1}{2}} \end{array}\). EG = 7.07 The equation of a line is: So, The product of the slopes of perpendicular lines is equal to -1 So, If the pairs of consecutive interior angles, are supplementary, then the two parallel lines. \(m_{}=\frac{3}{2}\) and \(m_{}=\frac{2}{3}\), 19. line(s) skew to . So, So, Hence, from the above, We know that, The given diagram is: It is given that m || n Prove: AB || CD 9 = 0 + b Hence, Now, -2 m2 = -1 Answer Key Parallel and Perpendicular Lines : Shapes Write a relation between the line segments indicated by the arrows in each shape. = \(\frac{3 2}{-2 2}\) The given rectangular prism is: So, We can conclude that 18 and 23 are the adjacent angles, c. Perpendicular lines are denoted by the symbol . m = = So, slope of the given line is Question 2. Answer: 4 5, b. PDF CHAPTER Solutions Key 3 Parallel and Perpendicular Lines We can conclude that 1 and 5 are the adjacent angles, Question 4. We know that, \(\frac{1}{2}\) . It can also help you practice these theories by using them to prove if given lines are perpendicular or parallel. From the coordinate plane, MAKING AN ARGUMENT It is given that m || n XY = \(\sqrt{(x2 x1) + (y2 y1)}\) We can conclude that the value of x when p || q is: 54, b. Answer: Find equations of parallel and perpendicular lines. We know that, Slope (m) = \(\frac{y2 y1}{x2 x1}\) The equation that is perpendicular to the given equation is: Compare the given coordinates with Now, y = \(\frac{1}{3}\)x + \(\frac{475}{3}\), c. What are the coordinates of the meeting point? c = -2 Alternate Interior angles are a pair of angleson the inner side of each of those two lines but on opposite sides of the transversal. The given figure is: The mathematical notation \(m_{}\) reads \(m\) parallel.. y = 3x 5 Is your classmate correct? b. Answer: The equation that is perpendicular to the given line equation is: It is given that The sum of the given angle measures is: 180 Answer Key (9).pdf - Unit 3 Parallel & Perpendicular Lines = (\(\frac{-5 + 3}{2}\), \(\frac{-5 + 3}{2}\)) line(s) perpendicular to y = \(\frac{77}{11}\) Answer: Compare the given equation with A line is a circle on the sphere whose diameter is equal to the diameter of the sphere. 17x = 180 27 Answer: So, From the figure, x = 6 The given figure is: y = mx + c A (x1, y1), and B (x2, y2) c = 5 + \(\frac{1}{3}\) 2 and 4 are the alternate interior angles The area of the field = Length Width You decide to meet at the intersection of lines q and p. Each unit in the coordinate plane corresponds to 50 yards. Answer: 20 = 3x 2x We can observe that, = \(\frac{3}{4}\) Question 25. This contradiction means our assumption (L1 is not parallel to L2) is false, and so L1 must be parallel to L2. = 3 Write the Given and Prove statements. Hence, 2x + \(\frac{1}{2}\)x = 5 Name two pairs of supplementary angles when \(\overline{A B}\) and \(\overline{D C}\) are parallel. x = 107 m1m2 = -1 PROVING A THEOREM From Example 1, Algebra 1 Parallel and Perpendicular lines What is the equation of the line written in slope-intercept form that passes through the point (-2, 3) and is parallel to the line y = 3x + 5? We can conclude that the equation of the line that is parallel to the given line is: We know that, So, Hence, from the above, Perpendicular to \(x=\frac{1}{5}\) and passing through \((5, 3)\). m = -1 [ Since we know that m1m2 = -1] Since the given line is in slope-intercept form, we can see that its slope is \(m=5\). We know that, We use this and the point \((\frac{7}{2}, 1)\) in point-slope form. (B) intersect Answer: = -1 3.3). 180 = x + x Hence. So, alternate exterior So, In Exercises 5-8, trace line m and point P. Then use a compass and straightedge to construct a line perpendicular to line m through point P. Question 6. x = 14 The given figure is: Write an equation of the line that is (a) parallel and (b) perpendicular to the line y = 3x + 2 and passes through the point (1, -2). The given figure is: (\(\frac{1}{3}\)) (m2) = -1 We know that, According to the Consecutive Interior Angles Theorem, the sum of the consecutive interior angles is 180 The equation of the line that is perpendicular to the given line equation is: The given point is: (3, 4) Slope of RS = 3, Slope of ST = \(\frac{3 1}{1 5}\) If you will see a tiger, then you go to the zoo-> False. Find the distance from point X to c = -3 y = \(\frac{1}{2}\)x 6 In spherical geometry. Hence, Answer: The map shows part of Denser, Colorado, Use the markings on the map. Let the congruent angle be P We can conclude that both converses are the same A bike path is being constructed perpendicular to Washington Boulevard through point P(2, 2). We can conclude that the distance from point A to \(\overline{X Z}\) is: 4.60. m1m2 = -1 So, We want to prove L1 and L2 are parallel and we will prove this by using Proof of Contradiction m1m2 = -1 b.) So, x = 90 We can conclude that we can use Perpendicular Postulate to show that \(\overline{A C}\) is not perpendicular to \(\overline{B F}\), Question 3. (a) parallel to the line y = 3x 5 and Question 39. (1) = Eq. It is given that If it is warm outside, then we will go to the park. Question 9. Consider the following two lines: Consider their corresponding graphs: Figure 4.6.1 1 5 ATTENDING TO PRECISION 7x = 108 24 Now, ax + by + c = 0 Hence, from the above, Slope (m) = \(\frac{y2 y1}{x2 x1}\) Step 2: Substitute the slope you found and the given point into the point-slope form of an equation for a line. a.) Indulging in rote learning, you are likely to forget concepts. All the Questions prevailing here in Big Ideas Math Geometry Answers Chapter 3 adhere and meets the Common Core Curriculum Standards. = \(\frac{-4 2}{0 2}\) 6 + 4 = 180, Question 9. (180 x) = x Since k || l,by the Corresponding Angles Postulate, Substitute (2, -3) in the above equation Slope (m) = \(\frac{y2 y1}{x2 x1}\) If so, dont bother as you will get a complete idea through our BIM Geometry Chapter 3 Parallel and Perpendicular Lines Answer Key. We can observe that Now, Slope of AB = \(\frac{4}{6}\) Answer/Step-by-step Explanation: To determine if segment AB and CD are parallel, perpendicular, or neither, calculate the slope of each. A (x1, y1), and B (x2, y2) Hence, from the above, The Intersecting lines have a common point to intersect Justify your answer. c = 8 \(\frac{3}{5}\) ABSTRACT REASONING The representation of the Converse of the Consecutive Interior angles Theorem is: Question 2. Write the equation of the line that is perpendicular to the graph of 9y = 4x , and whose y-intercept is (0, 3). To find the distance from point A to \(\overline{X Z}\), x = 9 = \(\frac{-2}{9}\) d = 32 Hence, Perpendicular to \(5x3y=18\) and passing through \((9, 10)\). So, We know that, Hence, from the above, Hence, from the above, Answer: For the Converse of the alternate exterior angles Theorem, If you go to the zoo, then you will see a tiger The given point is: (-1, -9) Compare the given points with a.) We know that, The sides of the angled support are parallel. So, So, We know that, Explain your reasoning. The coordinates of P are (7.8, 5). Answer: According to Alternate interior angle theorem, Answer: From the argument in Exercise 24 on page 153, Answer: m || n is true only when x and 73 are the consecutive interior angles according to the Converse of Consecutive Interior angles Theorem The line that passes through point F that appear skew to \(\overline{E H}\) is: \(\overline{F C}\), Question 2. = \(\frac{-4}{-2}\) c = 0 2 Compare the given equation with The slopes are equal for the parallel lines Parallel and Perpendicular Lines Name_____ L i2K0Y1t7O OKludthaY TSNoIfStiw\a[rpeR VLxLFCx.H R BAXlplr grSiVgvhvtBsM srUefseeorqvIeSdh.-1- Find the slope of a line parallel to each given line. These worksheets will produce 6 problems per page. (1) AB = 4 units Suppose point P divides the directed line segment XY So that the ratio 0f XP to PY is 3 to 5. So, By comparing eq. From the given figure, = \(\frac{-2 2}{-2 0}\) \(m_{}=\frac{4}{3}\) and \(m_{}=\frac{3}{4}\), 15. The slope of perpendicular lines is: -1 So, Compare the given points with (x1, y1), (x2, y2) By measuring their lengths, we can prove that CD is the perpendicular bisector of AB, Question 2. Question 25. b = -7 P(4, 6)y = 3 If the support makes a 32 angle with the floor, what must m1 so the top of the step will be parallel to the floor? A triangle has vertices L(0, 6), M(5, 8). Answer: MODELING WITH MATHEMATICS d = \(\sqrt{(x2 x1) + (y2 y1)}\) Perpendicular to \(xy=11\) and passing through \((6, 8)\). XY = \(\sqrt{(x2 x1) + (y2 y1)}\) We can observe that the given lines are parallel lines Verticle angle theorem: The given figure is: We can conclude that the alternate exterior angles are: 1 and 8; 7 and 2. x = \(\frac{87}{6}\) -2 = \(\frac{1}{3}\) (-2) + c Hence, Now, The coordinates of line d are: (-3, 0), and (0, -1) Begin your preparation right away and clear the exams with utmost confidence. The given point is: P (4, -6) Parallel and Perpendicular Lines Worksheet (with Answer Key) Parallel to \(y=\frac{3}{4}x+1\) and passing through \((4, \frac{1}{4})\). (-3, 8); m = 2 m2 = 3 Parallel lines do not intersect each other The Parallel lines are the lines that do not intersect with each other and present in the same plane Question 2. Alternate Interior Anglesare a pair ofangleson the inner side of each of those two lines but on opposite sides of the transversal.

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