6 (2y) 6(3) = 180 42 We know that, It is given that m || n Parallel to \(5x2y=4\) and passing through \((\frac{1}{5}, \frac{1}{4})\). c. y = 5x + 6 So, m = -1 [ Since we know that m1m2 = -1] y = \(\frac{1}{3}\)x \(\frac{8}{3}\). We can conclude that the distance from point A to the given line is: 8.48. Thus the slope of any line parallel to the given line must be the same, \(m_{}=5\). Answer: The Coincident lines may be intersecting or parallel Compare the above equation with The representation of the parallel lines in the coordinate plane is: Question 16. Now, -1 = \(\frac{1}{2}\) ( 6) + c Hence, 42 and 6(2y 3) are the consecutive interior angles Since it must pass through \((3, 2)\), we conclude that \(x=3\) is the equation. c = -5 The lines that do not intersect and are not parallel and are not coplanar are Skew lines It is given that a new road is being constructed parallel to the train tracks through points V. An equation of the line representing the train tracks is y = 2x. Substitute (3, 4) in the above equation Hence,f rom the above, So, Consider the following two lines: Both lines have a slope \(m=\frac{3}{4}\) and thus are parallel. The given equation is: The portion of the diagram that you used to answer Exercise 26 on page 130 is: Question 2. So, The two lines are Coincident when they lie on each other and are coplanar Step 4: Find the slope of a line perpendicular to each given line. The equation of a line is: We know that, Answer: We know that, Parallel lines are lines in the same plane that never intersect. Hence, The angles that have the same corner are called Adjacent angles Answer: Question 32. The coordinates of line c are: (4, 2), and (3, -1) Question 2. Given a b y = \(\frac{1}{4}\)x + c In Exercises 21 and 22, write and solve a system of linear equations to find the values of x and y. The given perpendicular line equations are: An engaging digital escape room for finding the equations of parallel and perpendicular lines. We can observe that when r || s, The given point is: A (2, -1) The given figure is: According to the Perpendicular Transversal Theorem, x = 29.8 From the above definition, Observe the following figure and the properties of parallel and perpendicular lines to identify them and differentiate between them. The sum of the angle measure between 2 consecutive interior angles is: 180 x = 6 So, Hence, from the above, We can conclude that the vertical angles are: Find the Equation of a Parallel Line Passing Through a Given Equation and Point Explain. 5 = 4 (-1) + b y = 2x and y = 2x + 5 Answer: Answer: The point of intersection = (-1, \(\frac{13}{2}\)) Compare the effectiveness of the argument in Exercise 24 on page 153 with the argument You can find the distance between any two parallel lines What flaw(s) exist in the argument(s)? 2x y = 4 Question 18. The resultant diagram is: A(1, 3), B(8, 4); 4 to 1 Slope (m) = \(\frac{y2 y1}{x2 x1}\) We get y = -2x + c Hence, from the above figure, The given points are: 3 + 133 = 180 (By using the Consecutive Interior angles theorem) d. AB||CD // Converse of the Corresponding Angles Theorem From the given figure, Therefore, these lines can be identified as perpendicular lines. = 0 Answer: Question 6. The slope of line a (m) = \(\frac{y2 y1}{x2 x1}\) m1m2 = -1 Compare the given equation with If p and q are the parallel lines, then r and s are the transversals The corresponding angles are: and 5; 4 and 8, b. alternate interior angles We can conclude that the plane parallel to plane LMQ is: Plane JKL, Question 5. The Coincident lines are the lines that lie on one another and in the same plane Question 13. Substitute P (4, -6) in the above equation So, The given figure is: We know that, Suppose point P divides the directed line segment XY So that the ratio 0f XP to PY is 3 to 5. So, y = -2x + c If we want to find the distance from the point to a given line, we need the perpendicular distance of a point and a line -5 = \(\frac{1}{2}\) (4) + c y = \(\frac{1}{4}\)x 7, Question 9. (1) Eq. Mark your diagram so that it cannot be proven that any lines are parallel. Answer: The vertical angles are: 1 and 3; 2 and 4 Slope (m) = \(\frac{y2 y1}{x2 x1}\) We know that, c = 6 0 If the slope of two given lines are negative reciprocals of each other, they are identified as perpendicular lines. Hence, 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. Answer: Answer: c. Use the properties of angles formed by parallel lines cut by a transversal to prove the theorem. So, m2 = \(\frac{1}{2}\) Answer: Answer the questions related to the road map. 3.3). Slope of ST = \(\frac{1}{2}\), Slope of TQ = \(\frac{3 6}{1 2}\) invest little times to right of entry this on-line notice Parallel And Perpendicular Lines Answer Key as capably as review them wherever you are now. We can conclude that We were asked to find the equation of a line parallel to another line passing through a certain point. By using the parallel lines property, We can conclude that the claim of your friend can be supported, Question 7. To find the value of c, We know that, So, 2017 a level econs answer 25x30 calculator Angle of elevation calculator find distance Best scientific calculator ios Let the given points are: x = 97 According to the Alternate Exterior angles Theorem, Question 1. Answer: Now, Question 30. y = \(\frac{1}{2}\)x 4, Question 22. PROOF Now, Answer: Save my name, email, and website in this browser for the next time I comment. Now, : n; same-side int. From the given figure, If the slope of AB and CD are the same value, then they are parallel. EG = \(\sqrt{(5) + (5)}\) The given figure is: Homework 2 - State whether the given pair are parallel, perpendicular, or intersecting. Substitute A (2, -1) in the above equation to find the value of c m2 = -1 The Alternate Interior Angles Theorem states that, when two parallel lines are cut by a transversal, the resultingalternate interior anglesare congruent Where, (7x 11) = (4x + 58) Substitute A (2, 0) in the above equation to find the value of c Question 1. The sum of the angle measures of a triangle is: 180 So, From the given figure, = 2 The equation for another line is: We have to find the distance between X and Y i.e., XY We can observe that Hence, Slope of AB = \(\frac{2}{3}\) Find an equation of line q. The given equation is: Draw a line segment CD by joining the arcs above and below AB PDF 3-7 Slopes of Parallel and Perpendicular Lines Hence, 3.3) AP : PB = 2 : 6 x = n m = = So, slope of the given line is Question 2. Answer: Question 26. Since you are given a point and the slope, use the point-slope form of a line to determine the equation. Hence, from the above, The given statement is: It is important to have a geometric understanding of this question. Compare the given equations with Using the same compass selling, draw an arc with center B on each side \(\overline{A B}\). Answer: Question 24. We can conclude that The Perpendicular lines are the lines that are intersected at the right angles y = -x + c Therefore, the final answer is " neither "! MODELING WITH MATHEMATICS \(\frac{5}{2}\)x = 5 Now, y = mx + c x = 29.8 and y = 132, Question 7. So, So, d = \(\sqrt{(x2 x1) + (y2 y1)}\) = \(\frac{15}{45}\) Use the steps in the construction to explain how you know that\(\overline{C D}\) is the perpendicular bisector of \(\overline{A B}\). The equation that is perpendicular to the given line equation is: From the given figure, 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 From the above figure, Hence, from the above, Substitute A (3, 4) in the above equation to find the value of c y = \(\frac{1}{5}\)x + c So, (5y 21) ad (6x + 32) are the alternate interior angles So, Select the angle that makes the statement true. Answer: 1 = 42 Verify your answer. Hence, y = \(\frac{1}{3}\)x + \(\frac{16}{3}\), Question 5. P( 4, 3), Q(4, 1) Slope of line 1 = \(\frac{-2 1}{-7 + 3}\) y = -3x 2 (2) = \(\frac{50 500}{200 50}\) The Alternate Interior angles are congruent When we observe the ladder, It is not always the case that the given line is in slope-intercept form. Explain why the tallest bar is parallel to the shortest bar. We can observe that If line E is parallel to line F and line F is parallel to line G, then line E is parallel to line G. Question 49. So, We know that, So, The consecutive interior angles are: 2 and 5; 3 and 8. The slopes are equal fot the parallel lines y = \(\frac{1}{2}\)x + c The given figure is: So, In a plane, if a line is perpendicular to one of the two parallel lines, then it is perpendicular to the other line also So, A Linear pair is a pair of adjacent angles formed when two lines intersect Then write Answer: Now, COMPLETE THE SENTENCE (x1, y1), (x2, y2) 0 = 2 + c A line is a circle on the sphere whose diameter is equal to the diameter of the sphere. Using P as the center and any radius, draw arcs intersecting m and label those intersections as X and Y. m2 = -1 To prove: l || k. Question 4. We know that, Hence, Given: k || l 3 = 47 Write the equation of the line that is perpendicular to the graph of 6 2 1 y = x + , and whose y-intercept is (0, -2). (50, 175), (500, 325) Answer: So, Now, Hence, from the above, Answer: Explain our reasoning. The given figure is: = \(\frac{11}{9}\) The points are: (-\(\frac{1}{4}\), 5), (-1, \(\frac{13}{2}\)) These worksheets will produce 6 problems per page. c = 8 Now, The equation that is perpendicular to the given equation is: Line 1: (1, 0), (7, 4) c = 2 + 2 2x = 3 The perpendicular line equation of y = 2x is: m1m2 = -1 The rope is pulled taut. In which of the following diagrams is \(\overline{A C}\) || \(\overline{B D}\) and \(\overline{A C}\) \(\overline{C D}\)? The given figure is: c = -4 Question 23. The slope of line a (m) = \(\frac{y2 y1}{x2 x1}\) In this form, you can see that the slope is \(m=2=\frac{2}{1}\), and thus \(m_{}=\frac{1}{2}=+\frac{1}{2}\). = 44,800 square feet 1 + 57 = 180 If the slope of one is the negative reciprocal of the other, then they are perpendicular. We can observe that the given lines are perpendicular lines You can prove that4and6are congruent using the same method. y = \(\frac{2}{3}\) Hence, from the above, = 2.23 Now, then they are congruent. = -1 Answer: Question 2. The coordinates of line 1 are: (10, 5), (-8, 9) = \(\frac{1}{-4}\) 2 = 122, Question 16. We know that, The equation for another perpendicular line is: The slope of PQ = \(\frac{y2 y1}{x2 x1}\) X (-3, 3), Y (3, 1) Question 3. Answer: You and your friend walk to school together every day. y = \(\frac{1}{2}\)x 6 We know that, We can observe that The given figure is: The parallel lines have the same slopes Hence, \(m_{}=\frac{2}{7}\) and \(m_{}=\frac{7}{2}\), 17. Each step is parallel to the step immediately above it. The distance that the two of you walk together is: Solution to Q6: No. Therefore, they are perpendicular lines. m2 = \(\frac{1}{2}\), b2 = 1 x = 12 and y = 7, Question 3. y = mx + b These Parallel and Perpendicular Lines Worksheets will ask the student to find the equation of a parallel line passing through a given equation and point. The equation that is perpendicular to y = -3 is: The equation of the line that is parallel to the given line equation is: For example, if the equations of two lines are given as, y = -3x + 6 and y = -3x - 4, we can see that the slope of both the lines is the same (-3). Two lines are cut by a transversal. x = \(\frac{-6}{2}\) = 3, The slope of line d (m) = \(\frac{y2 y1}{x2 x1}\) The adjacent angles are: 1 and 2; 2 and 3; 3 and 4; and 4 and 1 Each unit in the coordinate plane corresponds to 50 yards. We know that, 10) y = -2x 1 (2) We know that, So, 5y = 116 + 21 For the intersection point of y = 2x, The given figure is; We know that, Answer: Question 1. We can observe that Hence, from the above, Prove: c || d x = 12 Draw a diagram to represent the converse. Hence, from the above, Answer: Question 41. Definition of Parallel and Perpendicular Parallel lines are lines in the same plane that never intersect. For a square, 2y and 58 are the alternate interior angles We know that, = \(\sqrt{(3 / 2) + (3 / 4)}\) Answer: Slope (m) = \(\frac{y2 y1}{x2 x1}\) Hence, from the above, c = 4 PROVING A THEOREM So, In Example 4, the given theorem is Alternate interior angle theorem The given pair of lines are: y = -2x + c Hence, The given statement is: Answer: From the given figure, Eq. Parallel to \(y=\frac{1}{2}x+2\) and passing through \((6, 1)\). The given figure is: 2 + 10 = c These Parallel and Perpendicular Lines Worksheets are great for practicing identifying perpendicular lines from pictures. The parallel lines have the same slopes -2 = 3 (1) + c Answer: x = 9. Draw a diagram of at least two lines cut by at least one transversal. The give pair of lines are: y = 180 48 We know that, The coordinates of line a are: (2, 2), and (-2, 3) We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Now, c = \(\frac{37}{5}\) y = -2x + c y = \(\frac{3}{2}\)x + c Hence, from the above, We know that, Answer: Proof: By comparing the given equation with From the given figure, y = \(\frac{1}{2}\) (B) Alternate Interior Angles Converse (Thm 3.6) 3. Write the equation of a line that would be parallel to this one, and pass through the point (-2, 6). m2 = -2 The equation that is perpendicular to the given equation is: We know that, We get XY = \(\sqrt{(4.5) + (1)}\) Now, b. . Answer: -2 m2 = -1 Answer: For example, the figure below shows the graphs of various lines with the same slope, m= 2 m = 2. Now, \(\frac{8 (-3)}{7 (-2)}\) 2-4 Additional Practice Parallel And Perpendicular Lines Answer Key November 7, 2022 admin 2-4 Extra Observe Parallel And Perpendicular Strains Reply Key. Now, The slope is: 3 The given point is: (-3, 8) y= \(\frac{1}{3}\)x + 4 Substitute (2, -3) in the above equation Likewise, parallel lines become perpendicular when one line is rotated 90. = Undefined We know that, Answer: XY = \(\sqrt{(3 + 3) + (3 1)}\) If two lines are parallel to the same line, then they are parallel to each other We can observe that Since the given line is in slope-intercept form, we can see that its slope is \(m=5\). Section 6.3 Equations in Parallel/Perpendicular Form. Algebra 1 Writing Equations of Parallel and Perpendicular Lines 1) through: (2, 2), parallel to y = x + 4. Determine whether quadrilateral JKLM is a square. Explain your reasoning. Question 25. The equation of a line is: The given parallel line equations are: x = 97, Question 7. Explain why the top rung is parallel to the bottom rung. The given points are: x = \(\frac{24}{4}\) Slope of line 1 = \(\frac{9 5}{-8 10}\) Tell which theorem you use in each case. We know that, y = \(\frac{1}{3}\) (10) 4 Compare the given equation with 8x = 118 6 Eq. Work with a partner: The figure shows a right rectangular prism. Answer: Hence, What shape is formed by the intersections of the four lines? During a game of pool. The angle measures of the vertical angles are congruent So, We know that, We know that, From the above table, Point A is perpendicular to Point C Answer: Question 34. x = 60 Compare the given coordinates with (x1, y1), and (x2, y2) We can conclude that 1 = -3 (6) + b m = \(\frac{0 2}{7 k}\) = \(\sqrt{1 + 4}\) Draw \(\overline{A P}\) and construct an angle 1 on n at P so that PAB and 1 are corresponding angles Write an equation of a line perpendicular to y = 7x +1 through (-4, 0) Q. Answer: alternate interior Hence, \(\overline{I J}\) and \(\overline{C D}\), c. a pair of paralIeI lines Now, Answer: = \(\frac{-2}{9}\) Compare the given coordinates with So, The coordinates of the midpoint of the line segment joining the two houses = (150, 250) We can conclude that Question 21. So, Compare the given points with ATTENDING TO PRECISION Hence, from the above, Hence, A (x1, y1), and B (x2, y2) Explain your reasoning. Hence,f rom the above, To find the value of c, Perpendicular to \(5x3y=18\) and passing through \((9, 10)\). The product of the slopes of the perpendicular lines is equal to -1 So, Substitute P(-8, 0) in the above equation Are the numbered streets parallel to one another? Answer: = 320 feet It is given that The coordinates of line p are: So, Slopes of Parallel and Perpendicular Lines - ChiliMath c. Draw \(\overline{C D}\). The slope of the perpendicular line that passes through (1, 5) is: Which lines intersect ? Also, by the Vertical Angles Theorem, Answer: 4 5, b. c.) False, parallel lines do not intersect each other at all, only perpendicular lines intersect at 90. Parallel and Perpendicular Lines Worksheet - Mausmi Jadhav - TemplateRoller 2 = 133 No, p ||q and r ||s will not be possible at the same time because when p || q, r, and s can act as transversal and when r || s, p, and q can act as transversal. plane(s) parallel to plane ADE Graph the equations of the lines to check that they are parallel. So, We know that, We get Answer: m || n is true only when (7x 11) and (4x + 58) are the alternate interior angles by the Convesre of the Consecutive Interior Angles Theorem Substitute this slope and the given point into point-slope form. y = \(\frac{1}{3}\)x + \(\frac{475}{3}\), c. What are the coordinates of the meeting point? It is given that Answer: We know that, In Exercises 15 and 16, use the diagram to write a proof of the statement. Hence, 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. A(- 2, 1), B(4, 5); 3 to 7 1 and 8 Substitute A (3, -1) in the above equation to find the value of c Now, How are the Alternate Interior Angles Theorem (Theorem 3.2) and the Alternate Exterior Example 2: State true or false using the properties of parallel and perpendicular lines. Justify your answer for cacti angle measure. Make the most out of these preparation resources and stand out from the rest of the crowd. y = -2 (-1) + \(\frac{9}{2}\) Two nonvertical lines in the same plane, with slopes m1 and m2, are parallel if their slopes are the same, m1 = m2. Will the opening of the box be more steep or less steep? We know that, ANSWERS Page 53 Page 55 Page 54 Page 56g 5-6 Practice (continued) Form K Parallel and Perpendicular Lines Write an equation of the line that passes through the given point and is perpendicular to the graph of the given equation. The lines that are at 90 are Perpendicular lines The given coplanar lines are: Answer: Hence, from the above figure, alternate interior y = \(\frac{1}{2}\)x + c Let the given points are: The coordinates of P are (3.9, 7.6), Question 3. Inverses Tables Table of contents Parallel Lines Example 2 Example 3 Perpendicular Lines Example 1 Example 2 Example 3 Interactive The lines that are coplanar and any two lines that have a common point are called Intersecting lines \(\frac{6 (-4)}{8 3}\) x z and y z We can conclude that in order to jump the shortest distance, you have to jump to point C from point A. The points of intersection of parallel lines: So, It is given that the sides of the angled support are parallel and the support makes a 32 angle with the floor Name them. Hence, from the above, When finding an equation of a line perpendicular to a horizontal or vertical line, it is best to consider the geometric interpretation. We know that, Answer: Answer: AP : PB = 4 : 1 Hw Key Hw Part 2 key Updated 9/29/22 #15 - Perpendicular slope 3.6 (2017) #16 - Def'n of parallel 3.1 . Parallel and perpendicular lines have one common characteristic between them. The coordinates of the line of the second equation are: (1, 0), and (0, -2) The representation of the given point in the coordinate plane is: Question 56. Answer: We can observe that, From the given figure, Question 39. So, So, We can conclude that the distance from point A to the given line is: 5.70, Question 5. If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles formed are supplementary Substitute (4, 0) in the above equation From the above figure, 3 = 68 and 8 = (2x + 4) Parallel to \(y=\frac{1}{4}x5\) and passing through \((2, 1)\). x = \(\frac{40}{8}\) So, We can observe that, WHICH ONE did DOESNT BELONG? In Exercises 11 and 12. prove the theorem. P = (7.8, 5) -5 8 = c The representation of the Converse of Corresponding Angles Theorem is: b. Alternate Interior Angles Theorem (Theorem 3.2): If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. Parallel and Perpendicular Lines Maintaining Mathematical Proficiency Find the slope of the line. The given figure is: Slope (m) = \(\frac{y2 y1}{x2 x1}\) 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). = 1 If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent Compare the given points with Answer: y = \(\frac{1}{2}\)x \(\frac{1}{2}\), Question 10. Slope of QR = \(\frac{1}{2}\), Slope of RS = \(\frac{1 4}{5 6}\) 2x = 108 The given equation is: What is the perimeter of the field? We know that, The equation that is perpendicular to the given line equation is: The given statement is: A new road is being constructed parallel to the train tracks through points V. An equation of the line representing the train tracks is y = 2x. The given point is: A (-3, 7) The slopes of the parallel lines are the same b. To find 4: Do you support your friends claim? Is your friend correct? Explain your reasoning. -2 = \(\frac{1}{2}\) (2) + c From the figure, We know that, b. Answer: 2x + 72 = 180 Write an equation of the line passing through the given point that is parallel to the given line. (A) are parallel. So, x = \(\frac{120}{2}\) Great learning in high school using simple cues. DOC Geometry - Loudoun County Public Schools 11 and 13 XY = 6.32 We can observe that not any step is intersecting at each other From the given figure, y = -3x + 650, b. Perpendicular to \(x=\frac{1}{5}\) and passing through \((5, 3)\). y y1 = m (x x1) Click here for More Geometry Worksheets So, 4. Is your classmate correct? The coordinates of the school = (400, 300) Hence, from the above, The equation of the line that is perpendicular to the given line equation is: So, The equation of a line is: 2x = 135 15 So, The angles that are opposite to each other when two lines cross are called Vertical angles Using the properties of parallel and perpendicular lines, we can answer the given questions. 2x = 180 72 Answer: The equation of a line is: = (\(\frac{-2}{2}\), \(\frac{-2}{2}\)) We know that, Expert-Verified Answer The required slope for the lines is given below. = \(\frac{-2 2}{-2 0}\) We can also observe that w and z is not both to x and y ABSTRACT REASONING BCG and __________ are consecutive interior angles. A student says. 1 = 41. A(6, 1), y = 2x + 8 By the Vertical Angles Congruence Theorem (Theorem 2.6). So, 9+ parallel and perpendicular lines maze answer key pdf most standard The lines that have the same slope and different y-intercepts are Parallel lines Answer: Perpendicular Postulate: So, Parallel and Perpendicular Lines Worksheets - Math Worksheets Land The coordinates of y are the same. We know that, We know that, To find the value of c, We know that, We know that, a. The lines that do not intersect or not parallel and non-coplanar are called Skew lines 2x = 120 Answer: From the given figure, From the figure, Hence, from the above figure, Question 12. So, The given equation is: The given equation of the line is: are parallel, or are the same line. We know that, Answer: x = 9 We know that, Hence, We know that, From the given figure, Answer: MODELING WITH MATHEMATICS = \(\sqrt{31.36 + 7.84}\) The Converse of the Alternate Exterior Angles Theorem states that if alternate exterior anglesof two lines crossed by a transversal are congruent, then the two lines are parallel. Now, We can conclude that the value of k is: 5. 2 = 140 (By using the Vertical angles theorem) So, y = 132 Hence, from the above, 3m2 = -1 The given equation is: Give four examples that would allow you to conclude that j || k using the theorems from this lesson. Alternate Exterior angle Theorem: Now, The slope of the parallel equations are the same A(15, 21), 5x + 2y = 4 It is given that E is to \(\overline{F H}\) Given: k || l, t k 1 + 2 = 180 Part 1: Determine the parallel line using the slope m = {2 \over 5} m = 52 and the point \left ( { - 1, - \,2} \right) (1,2). Converse: Substitute A (-2, 3) in the above equation to find the value of c Explain. y = -2x + \(\frac{9}{2}\) (2) Hence, from the above, The equation of line q is: Name the line(s) through point F that appear skew to . Converse: For parallel lines, So, Can you find the distance from a line to a plane? Given m1 = 105, find m4, m5, and m8. We can conclude that the given statement is not correct. XY = \(\sqrt{(x2 x1) + (y2 y1)}\) a. m5 + m4 = 180 //From the given statement You are designing a box like the one shown. 3x 5y = 6 y = mx + b Hence, from the given figure, The given figure is: d = \(\sqrt{(300 200) + (500 150)}\) We can observe that the given lines are perpendicular lines We know that, So, From Exploration 1, y = x 6 We can observe that the slopes are the same and the y-intercepts are different a. According to Corresponding Angles Theorem, XY = \(\sqrt{(6) + (2)}\) m = 2 So, Answer: k 7 = -2 These worksheets will produce 6 problems per page. So, Compare the given equation with The given figure is: If the line cut by a transversal is parallel, then the corresponding angles are congruent We can conclude that So, x = 4 and y = 2 R and s, parallel 4. Write an equation of the line that passes through the given point and is parallel to the Get the best Homework key Find an equation of the line representing the bike path. The line through (k, 2) and (7, 0) is perpendicular to the line y = x \(\frac{28}{5}\). Hence, 8 6 = b The given point is: A (-6, 5) The Converse of the Alternate Interior Angles Theorem states that if two lines are cut by a transversal and the alternate interior anglesare congruent, then the lines are parallel Hence, from the above, A1.3.1 Write an equation of a line when given the graph of the line, a data set, two points on the line, or the slope and a point of the line; A1.3.2 Describe and calculate the slope of a line given a data set or graph of a line, recognizing that the slope is the rate of change; A1.3.6 . In spherical geometry, all points are points on the surface of a sphere. Quick Link for All Parallel and Perpendicular Lines Worksheets, Detailed Description for All Parallel and Perpendicular Lines Worksheets. 2 = 150 (By using the Alternate exterior angles theorem) Answer: Find the equation of the line passing through \((3, 2)\) and perpendicular to \(y=4\). x and 61 are the vertical angles m = 2 The angle at the intersection of the 2 lines = 90 0 = 90 The slope of the line that is aprallle to the given line equation is: The pair of lines that are different from the given pair of lines in Exploration 2 are: b is the y-intercept Hence, from the above, We can conclude that the value of x is: 133, Question 11. 2 and 3 are vertical angles a. Find an equation of the line representing the new road. Now, Answer: We can conclude that the alternate interior angles are: 4 and 5; 3 and 6, Question 14. = \(\frac{45}{15}\) c = -2 m1m2 = -1 m || n is true only when 3x and (2x + 20) are the corresponding angles by using the Converse of the Corresponding Angles Theorem