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From the given figure, Hence, Answer: The slope of the given line is: m = -2 (1) = Eq. From the given figure, The given figure is: We can observe that The equation of the line that is parallel to the given line is: So, Find an equation of the line representing the new road. Find the measure of the missing angles by using transparent paper. x = \(\frac{149}{5}\) To be proficient in math, you need to make conjectures and build a logical progression of statements to explore the truth of your conjectures. If m1 = 58, then what is m2? m = \(\frac{-30}{15}\) y = 12 c = -3 The letter A has a set of perpendicular lines. So, Hence. Answer: Slope of Parallel and Perpendicular Lines Worksheets Homework 2 - State whether the given pair are parallel, perpendicular, or intersecting. The given point is: P (3, 8) -9 = \(\frac{1}{3}\) (-1) + c y = -2x Cops the diagram with the Transitive Property of Parallel Lines Theorem on page 141. We can conclude that the given pair of lines are coincident lines, Question 3. ABSTRACT REASONING Slope (m) = \(\frac{y2 y1}{x2 x1}\) We can conclude that the values of x and y are: 9 and 14 respectively. From Example 1, Question 11. The given figure is: Geometrically, we note that if a line has a positive slope, then any perpendicular line will have a negative slope. Question: What is the difference between perpendicular and parallel? Hence, from the above, MATHEMATICAL CONNECTIONS 2x = -6 When we compare the given equation with the obtained equation, { "3.01:_Rectangular_Coordinate_System" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.02:_Graph_by_Plotting_Points" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.03:_Graph_Using_Intercepts" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.04:_Graph_Using_the_y-Intercept_and_Slope" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.05:_Finding_Linear_Equations" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.06:_Parallel_and_Perpendicular_Lines" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.07:_Introduction_to_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.08:_Linear_Inequalities_(Two_Variables)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.0E:_3.E:_Review_Exercises_and_Sample_Exam" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, { "00:_Front_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "01:_Real_Numbers_and_Their_Operations" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "02:_Linear_Equations_and_Inequalities" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "03:_Graphing_Lines" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "04:_Solving_Linear_Systems" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "05:_Polynomials_and_Their_Operations" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "06:_Factoring_and_Solving_by_Factoring" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "07:_Rational_Expressions_and_Equations" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "08:_Radical_Expressions_and_Equations" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "09:_Solving_Quadratic_Equations_and_Graphing_Parabolas" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "10:_Appendix_-_Geometric_Figures" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "zz:_Back_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, [ "article:topic", "license:ccbyncsa", "showtoc:no", "authorname:anonymous", "licenseversion:30", "program:hidden" ], https://math.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fmath.libretexts.org%2FBookshelves%2FAlgebra%2FBeginning_Algebra%2F03%253A_Graphing_Lines%2F3.06%253A_Parallel_and_Perpendicular_Lines, \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}}}\) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\), Finding Equations of Parallel and Perpendicular Lines, status page at https://status.libretexts.org. x = \(\frac{40}{8}\) For a pair of lines to be parallel, the pair of lines have the same slope but different y-intercepts An equation of the line representing the nature trail is y = \(\frac{1}{3}\)x 4. The given equation is: We can observe that the product of the slopes are -1 and the y-intercepts are different 4 = 5 This contradicts what was given,that angles 1 and 2 are congruent. The slopes of the parallel lines are the same We can observe that the given lines are perpendicular lines We know that, We can observe that PROOF Answer: Label the intersection as Z. Question 25. The equation for another perpendicular line is: Slope of TQ = 3 Answer: We know that, Answer: Question 32. Intersecting lines can intersect at any . From the above figure, It is given that 42 = (8x + 2) We know that, Substitute the given point in eq. Perpendicular to \(x=\frac{1}{5}\) and passing through \((5, 3)\). So, If p and q are the parallel lines, then r and s are the transversals 2x + 72 = 180 CRITICAL THINKING m2 = -1 Parallel lines are those that never intersect and are always the same distance apart. Now, Hence, Answer Key (9).pdf - Unit 3 Parallel & Perpendicular Lines y = -2x + c We can conclude that So, The postulates and theorems in this book represent Euclidean geometry. Which lines(s) or plane(s) contain point G and appear to fit the description? The given statement is: m1m2 = -1 From the given figure, From the given graph, Parallel and Perpendicular Lines Perpendicular Lines Two nonvertical lines are perpendicular if their slopes are opposite reciprocals of each other. Name two pairs of supplementary angles when \(\overline{A B}\) and \(\overline{D C}\) are parallel. We know that, the equation that is perpendicular to the given line equation is: It is given that 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 Explain why or why not. The coordinates of P are (7.8, 5). A (-3, -2), and B (1, -2) Question 37. For example, the figure below shows the graphs of various lines with the same slope, m= 2 m = 2. USING STRUCTURE If the pairs of alternate exterior angles. Compare the given points with First, find the slope of the given line. We can conclude that 1 = 2 We can conclude that the lines x = 4 and y = 2 are perpendicular lines, Question 6. Answer: Substitute (4, -5) in the above equation (-3, 7), and (8, -6) The sum of the angle measure between 2 consecutive interior angles is: 180 x + 73 = 180 By using the Vertical Angles Theorem, It is given that a student claimed that j K, j l The conjecture about \(\overline{A O}\) and \(\overline{O B}\) is: .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. a. Hence, from the above, Determine the slope of a line parallel to \(y=5x+3\). So, Answer: So, So, So, Newest Parallel And Perpendicular Lines Questions - Wyzant Answer: Question 24. b.) We can observe that Embedded mathematical practices, exercises provided make it easy for you to understand the concepts quite quickly. 3.6 Slopes of Parallel and Perpendicular Lines - GEOMETRY Now, The given equation is: = -3 XY = 4.60 Finding Parallel and Perpendicular Lines - mathsisfun.com So, The equation that is parallel to the given equation is: So, Hence, Given: k || l, t k Now, Answer: x = -3 Question 3. Answer: y = \(\frac{1}{2}\)x 3 Answer: So, Answer: We can conclude that both converses are the same Prove: c || d Write an equation of a line parallel to y = x + 3 through (5, 3) Q. c. m5=m1 // (1), (2), transitive property of equality The product of the slopes of perpendicular lines is equal to -1 So, y = 180 48 Vertical and horizontal lines are perpendicular. For parallel lines, We can conclude that the top rung is parallel to the bottom rung. y = 13 Hence, 17x + 27 = 180 ABSTRACT REASONING 13) y = -5x - 2 14) y = -1 G P2l0E1Q6O GKouHttad wSwoXfptiwlaer`eU yLELgCH.r C DAYlblQ wrMiWgdhstTsF wr_eNsVetrnv[eDd\.x B kMYa`dCeL nwHirtmhI KILnqfSisnBiRt`ep IGAeJokmEeCtPr[yY. The points are: (-9, -3), (-3, -9) 4 ________ b the Alternate Interior Angles Theorem (Thm. During a game of pool. The coordinates of the line of the second equation are: (1, 0), and (0, -2) as shown. . Using X and Y as centers and an appropriate radius, draw arcs that intersect. 2 and 3 are vertical angles y = \(\frac{7}{2}\) 3 Question 38. If two angles form a linear pair. The equation of the perpendicular line that passes through the midpoint of PQ is: The following summaries about parallel and perpendicular lines maze answer key pdf will help you make more personal choices about more accurate and faster information. We can observe that the given angles are corresponding angles Which values of a and b will ensure that the sides of the finished frame are parallel.? Step 5: Therefore, the final answer is " neither "! P( 4, 3), Q(4, 1) We can conclude that AC || DF, Question 24. We know that, Compare the given equation with ERROR ANALYSIS Slope of the line (m) = \(\frac{-2 + 2}{3 + 1}\) line(s) skew to . -2 = \(\frac{1}{2}\) (2) + c Compare the given equation with x = 97, Question 7. Answer: Question 2. How do you know that n is parallel to m? The given point is:A (6, -1) These worksheets will produce 6 problems per page. We know that, Let the given points are: x y + 4 = 0 ABSTRACT REASONING Hence, from the above, Question 23. Question 4. Answer: x 2y = 2 Answer: Answer: Answer: We can observe that the plane parallel to plane CDH is: Plane BAE. From the given figure, Alternate Interior Angles are a pair of angleson the inner side of each of those two lines but on opposite sides of the transversal. Alternate exterior anglesare the pair ofanglesthat lie on the outer side of the two parallel lines but on either side of the transversal line Hence, from the above, The coordinates of line d are: (0, 6), and (-2, 0) \(\frac{1}{3}\)m2 = -1 (11y + 19) and 96 are the corresponding angles So, a. The slopes of the parallel lines are the same Explain your reasoning. that passes through the point (2, 1) and is perpendicular to the given line. y 175 = \(\frac{1}{3}\) (x -50) 3 = 47 According to the Consecutive Interior Angles Theorem, the sum of the consecutive interior angles is 180 Answer: Question 24. The alternate interior angles are: 3 and 5; 2 and 8, c. alternate exterior angles We can conclude that the pair of perpendicular lines are: Think of each segment in the figure as part of a line. Hence, We can conclude that 1 = 60. Geometry parallel and perpendicular lines answer key Possible answer: 1 and 3 b. We have to find the point of intersection y = mx + c Hence, from the above, These worksheets will produce 6 problems per page. So, So, m2 = \(\frac{1}{2}\), b2 = 1 The given figure is: Hence, from the above, You started solving the problem by considering the 2 lines parallel and two lines as transversals The given point is: A (8, 2) Now, PDF ANSWERS We can conclude that the length of the field is: 320 feet, b. Unit 3 parallel and perpendicular lines homework 5 answer key 5 = 4 (-1) + b Perpendicular to \(y3=0\) and passing through \((6, 12)\). 2 = 180 47 y = -2x + 2 1 = 76, 2 = 104, 3 = 76, and 4 = 104, Work with a partner: Use dynamic geometry software to draw two parallel lines. y = 3x + c 3.3). Answer: 11y = 77 Hence, from the above, = 2.12 -5 = \(\frac{1}{4}\) (-8) + b The product of the slopes is -1 and the y-intercepts are different So, We can conclude that the value of XZ is: 7.07, Find the length of \(\overline{X Y}\) The equation of a line is: We know that, Question 2. Answer: We know that, Step 3: The slope of the perpendicular line that passes through (1, 5) is: 2 = 122 We know that, THOUGHT-PROVOKING Answer: Question 16. EG = \(\sqrt{(5) + (5)}\) 1 = 80 They are always the same distance apart and are equidistant lines. d = \(\sqrt{(13 9) + (1 + 4)}\) Substitute the given point in eq. 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. Substitute (1, -2) in the above equation Answer: Perpendicular lines have slopes that are opposite reciprocals, so remember to find the reciprocal and change the sign. So, x = 2 Now, From the figure, By comparing the given pair of lines with 3 = 53.7 and 4 = 53.7 1 = -18 + b Question 1. Two nonvertical lines in the same plane, with slopes m1 and m2, are parallel if their slopes are the same, m1 = m2. Explain your reasoning. We know that, Answer: Answer: Question 14. The pair of lines that are different from the given pair of lines in Exploration 2 are: It is given that So, We can conclude that there are not any parallel lines in the given figure. d = \(\sqrt{(x2 x1) + (y2 y1)}\) In Exploration 2, To find the y-intercept of the equation that is parallel to the given equation, substitute the given point and find the value of c For a pair of lines to be coincident, the pair of lines have the same slope and the same y-intercept Explain our reasoning. In a plane, if a line is perpendicular to one of two parallellines, then it is perpendicular to the other line also. Find the equation of the line passing through \((1, 5)\) and perpendicular to \(y=\frac{1}{4}x+2\). answer choices y = -x + 4 y = x + 6 y = 3x - 5 y = 2x Question 6 300 seconds Q. Answer: We can conclude that 8 right angles are formed by two perpendicular lines in spherical geometry. y = 4x + 9, Question 7. Repeat steps 3 and 4 below AB an equation of the line that passes through the midpoint and is perpendicular to \(\overline{P Q}\). y = 2x A(3, 1), y = \(\frac{1}{3}\)x + 10 Ruler: The highlighted lines in the scale (ruler) do not intersect or meet each other directly, and are the same distance apart, therefore, they are parallel lines. Perpendicular lines intersect at each other at right angles The equation that is perpendicular to the given line equation is: Parallel and perpendicular lines have one common characteristic between them. We can say that any coincident line do not intersect at any point or intersect at 1 point m = 3 From the given figure, Answer: Answer: Question 4. c. Consecutive Interior angles Theorem, Question 3. 12y 18 = 138 y = \(\frac{13}{2}\) Answer: We know that, For a vertical line, We can conclude that 2x + \(\frac{1}{2}\)x = 5 then they intersect to form four right angles. By using the Consecutive Interior Angles Theorem, d = | 2x + y | / \(\sqrt{5}\)} To find the value of b, We know that, We can conclude that both converses are the same Explain. m2 = -1 We can conclude that d = | ax + by + c| /\(\sqrt{a + b}\) So, d = | 2x + y | / \(\sqrt{2 + (1)}\) y = \(\frac{1}{2}\)x + 5 We can conclude that the distance from point E to \(\overline{F H}\) is: 7.07. Given: k || l Hence, from the above, From the given figure, COMPLETE THE SENTENCE We know that, In Exercise 31 on page 161, from the coordinate plane, Hence, from the above, The 2 pair of skew lines are: q and p; l and m, d. Prove that 1 2. Answer: The given point is: (-8, -5) In Exercises 21 and 22, write and solve a system of linear equations to find the values of x and y. The lines that have the slopes product -1 and different y-intercepts are Perpendicular lines Because j K, j l What missing information is the student assuming from the diagram? Answer: Hence, from the above, According to the Transitive Property of parallel lines, The slopes of the parallel lines are the same We can conclude that the value of x is: 14. (-1) (m2) = -1 Work with a partner: Fold a piece of pair in half twice. Answer Keys - These are for all the unlocked materials above. When you look at perpendicular lines they have a slope that are negative reciprocals of each other. Answer: Question 20. 7x = 84 Parallel lines are those lines that do not intersect at all and are always the same distance apart. x + 2y = 10 Given 1 2, 3 4 Hence, from the above, The y-intercept is: 9. Compare the given points with (x1, y1), (x2, y2) We can conclude that the perimeter of the field is: 920 feet, c. Turf costs $2.69 per square foot. Question 17. The parallel line equation that is parallel to the given equation is: Justify your answer. Hence, from the above, Question 27. When two lines are cut by a transversal, the pair ofangles on one side of the transversal and inside the two lines are called the Consecutive interior angles The given point is: P (4, -6) From the Consecutive Exterior angles Converse, y = 2x and y = 2x + 5 The equation that is perpendicular to y = -3 is: Substitute this slope and the given point into point-slope form. By using the Corresponding Angles Theorem, The pair of angles on one side of the transversal and inside the two lines are called the Consecutive interior angles. The equation that is perpendicular to the given line equation is: Part 1: Determine the parallel line using the slope m = {2 \over 5} m = 52 and the point \left ( { - 1, - \,2} \right) (1,2). -1 = \(\frac{1}{3}\) (3) + c We can observe that Now, Question 25. So, The perpendicular line equation of y = 2x is: To find the value of c, Answer: c = -2 We can conclude that the given lines are parallel. Explain why the top rung is parallel to the bottom rung. Decide whether it is true or false. y = \(\frac{1}{4}\)x 7, Question 9. = \(\frac{45}{15}\) The coordinates of line a are: (2, 2), and (-2, 3) Using the properties of parallel and perpendicular lines, we can answer the given questions. So, The converse of the given statement is: In Exercises 9 12, tell whether the lines through the given points are parallel, perpendicular, or neither. b) Perpendicular to the given line: Find the value of y that makes r || s. Now, c = 12 Hence, from the above, We can conclude that the value of x is: 60, Question 6. For the intersection point of y = 2x, So, Work with a partner: The figure shows a right rectangular prism. y = -2x + b (1) The given figure is: y = \(\frac{2}{3}\) By the _______ . y = -x + c To find the value of b, 2 = 180 123 A(- 3, 2), B(5, 4); 2 to 6 Hence, from the above, It is given that 3.3) Question 25. Our Parallel and Perpendicular Lines Worksheets are free to download, easy to use, and very flexible. From the given figure, Question 11. To find the coordinates of P, add slope to AP and PB XY = \(\sqrt{(x2 x1) + (y2 y1)}\) Question 13. y = -2x + c 2x + y + 18 = 180 y = \(\frac{1}{2}\) Answer: Given a Pair of Lines Determine if the Lines are Parallel, Perpendicular, or Intersecting The given point is: A (3, -4) From the converse of the Consecutive Interior angles Theorem, Answer: So, Answer: 1 = 2 = 133 and 3 = 47. From the given figure, Answer: So, Hence, Hence, To find the value of b, We know that, So, Hence, from the above, Substitute A (0, 3) in the above equation The angles are (y + 7) and (3y 17) We can observe that The given figure is: The parallel lines do not have any intersecting points Label the ends of the crease as A and B. Compare the given points with (x1, y1), and (x2, y2) Identify an example on the puzzle cube of each description. Hence, from the above, We can observe that not any step is intersecting at each other y = -3x + 19, Question 5. No, your friend is not correct, Explanation: Now, 1 = 2 = 123, Question 11. Answer: P(2, 3), y 4 = 2(x + 3) (2x + 20)= 3x We can conclude that in order to jump the shortest distance, you have to jump to point C from point A. The given equations are: We can conclude that the parallel lines are: We can conclude that a line equation that is perpendicular to the given line equation is: We know that, y = \(\frac{5}{3}\)x + c One way to build stairs is to attach triangular blocks to angled support, as shown. So, m2 = \(\frac{2}{3}\) Hence, from the given figure, Let's expand 2 (x 5) and then rearrange: y 4 = 2x 10. The equation of the line that is perpendicular to the given line equation is: We can conclude that 44 and 136 are the adjacent angles, b. The standard form of the equation is: Any fraction that contains 0 in the numerator has its value equal to 0 y = mx + c 1 4. Given: m5 + m4 = 180 m2 and m3 So, Justify your answer for cacti angle measure. Answer: So, The intersection point of y = 2x is: (2, 4) AC is not parallel to DF. From the given figure, x = y = 29, Question 8. Find the Equation of a Parallel Line Passing Through a Given Equation and Point F if two coplanar strains are perpendicular to the identical line then the 2 strains are. = 255 yards We know that, We know that, State which theorem(s) you used. y = \(\frac{1}{2}\)x + 8, Question 19. Substitute (-5, 2) in the given equation The equation that is perpendicular to the given line equation is: If two lines are horizontal, then they are parallel Now, 12y = 138 + 18 Question 23. The point of intersection = (\(\frac{3}{2}\), \(\frac{3}{2}\)) The given figure is: We can conclude that m || n by using the Corresponding Angles Theorem, Question 14. Answer: Answer: A student says. Justify your conjecture. We can conclude that the consecutive interior angles are: 3 and 5; 4 and 6, Question 6. PDF Infinite Algebra 1 - Parallel & Perpendicular Slopes & Equations of Lines Answer: Answer: Definition of Parallel and Perpendicular Parallel lines are lines in the same plane that never intersect. (13, 1), and (9, -4) How are the slopes of perpendicular lines related? a. m1 + m8 = 180 //From the given statement The Intersecting lines have a common point to intersect To find the distance from line l to point X, Now, We can conclude that the alternate interior angles are: 4 and 5; 3 and 6, Question 14. So, Classify the pairs of lines as parallel, intersecting, coincident, or skew. Since k || l,by the Corresponding Angles Postulate, x = 6 Decide whether there is enough information to prove that m || n. If so, state the theorem you would use. \(\overline{I J}\) and \(\overline{C D}\), c. a pair of paralIeI lines Answer: Which pair of angle measures does not belong with the other three? (C) are perpendicular We know that, From the above figure, So, We can observe that the given lines are perpendicular lines The two lines are Intersecting when they intersect each other and are coplanar Answer: 1 and 8 are vertical angles Hence, from the above, Answer: When we compare the actual converse and the converse according to the given statement, Explain your reasoning. Now, We can conclude that the pair of parallel lines are: Parallel to \(x+4y=8\) and passing through \((1, 2)\). 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. So, So, So, A hand rail is put in alongside the steps of a brand new home as proven within the determine. Answer: In Exploration 3. find AO and OB when AB = 4 units. With Cuemath, you will learn visually and be surprised by the outcomes. y = x + c Step 2: (b) perpendicular to the given line. So, b.) The slope of the equation that is parallel t the given equation is: \(\frac{1}{3}\) Question 29. The slopes of parallel lines, on the other hand, are exactly equal. The given equation is: Answer: Lines l and m are parallel.