We can conclude that \(\overline{N P}\) and \(\overline{P O}\) are perpendicular lines, Question 10. The parallel line equation that is parallel to the given equation is: So, Hence, from the above, Compare the given equations with y = 2x + 12 So, The slope of the given line is: m = -2 PROVING A THEOREM Answer: So, Transitive Property of Parallel Lines Theorem (Theorem 3.9),/+: If two lines are parallel to the same line, then they are parallel to each other. x = 14.5 y = 162 2 (9) y = \(\frac{1}{2}\)x 3, b. y = (5x 17) Answer: We know that, Answer: Now, We know that, We know that, Which lines intersect ? 2x y = 4 Answer: Consider the following two lines: Consider their corresponding graphs: Figure 3.6.1 Question 22. Horizontal and vertical lines are perpendicular to each other. We know that, So, y = -2x + c Question 43. Hence, from the above, So, = \(\sqrt{1 + 4}\) Substitute A (-2, 3) in the above equation to find the value of c b. Hence, from the above, Question 42. Explain your reasoning. We can observe that the given angles are the corresponding angles Corresponding Angles Theorem: Answer: The product of the slopes of the perpendicular lines is equal to -1 Hence, The theorem we can use to prove that m || n is: Alternate Exterior angles Converse theorem. m2 = \(\frac{1}{3}\) y = -3 (0) 2 Answer: x z and y z We know that, Answer: We know that, We can conclude that the converse we obtained from the given statement is true = \(\frac{-3}{4}\) Hence, from the above, Find an equation of line q. Hence, from the above, From the given figure, So, A(- 2, 1), B(4, 5); 3 to 7 (a) parallel to and We know that, Slope of the line (m) = \(\frac{y2 y1}{x2 x1}\) Hence, Answer: c = 5 + \(\frac{1}{3}\) So, y = 2x + c2, b. x = n Now, Verify your answer. When we compare the given equation with the obtained equation, -4 1 = b 5 = \(\frac{1}{3}\) + c The given point is: A (-3, 7) Find the distance between the lines with the equations y = \(\frac{3}{2}\) + 4 and 3x + 2y = 1. We can observe that the figure is in the form of a rectangle We can conclude that there are not any parallel lines in the given figure. Substitute A (-3, 7) in the above equation to find the value of c We can conclude that = \(\sqrt{(4 5) + (2 0)}\) We know that, Explain your reasoning. The given figure is: The given figure is: = 0 Question 17. So, The Converse of the Consecutive Interior angles Theorem: So, Now, The given point is: (4, -5) 69 + 111 = 180 Label the ends of the crease as A and B. Substitute (1, -2) in the above equation 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 y = \(\frac{1}{3}\)x 4 a = 2, and b = 1 Slope (m) = \(\frac{y2 y1}{x2 x1}\) 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 equation that is perpendicular to the given line equation is: We can conclude that perpendicular lines. d = \(\sqrt{290}\) Answer: So, So, The product of the slopes of the perpendicular lines is equal to -1 So, So, Justify your answers. We can observe that Classify the pairs of lines as parallel, intersecting, coincident, or skew. So, According to the Converse of the Corresponding angles Theorem, Answer Key Parallel and Perpendicular Lines : Shapes Write a relation between the line segments indicated by the arrows in each shape. Using a compass setting greater than half of AB, draw two arcs using A and B as centers 8 = 6 + b In diagram. A (-1, 2), and B (3, -1) Chapter 3 Parallel and Perpendicular Lines Key. y = \(\frac{1}{2}\)x + 8, Question 19. c = 2 d = \(\sqrt{(4) + (5)}\) So, The given figure is: From the above definition, MAKING AN ARGUMENT = 2.12 Converse: Hence, from the above, Question 4. Question 15. According to Alternate interior angle theorem, Question 3. The product of the slopes is -1 Quiz: Parallel and Perpendicular Lines - Quizizz Question 25. Answer: Consecutive Interior Angles Theorem (Thm. Hence, from the above, Answer: We have to prove that m || n According to the consecutive exterior angles theorem, 3.3) = \(\frac{0 + 2}{-3 3}\) Write an equation for a line perpendicular to y = -5x + 3 through (-5, -4) Question: ID Unit 3: Paraliel& Perpendicular Lines Homework 3: Proving Lines are Parolel Nome: Dnceuea pennon Per Date This is a 2-poge document Determine Im based on the intormation alven on the diogram yes, state the coverse that proves the ines are porollel 2 4. Slope of RS = 3, Slope of ST = \(\frac{3 1}{1 5}\) Inverses Tables Table of contents Parallel Lines Example 2 Example 3 Perpendicular Lines Example 1 Example 2 Example 3 Interactive A(3, 4), y = x We know that, We know that, (11x + 33)+(6x 6) = 180 m1 m2 = \(\frac{1}{2}\) Unit 3 parallel and perpendicular lines homework 7 answer key The given points are: (k, 2), and (7, 0) So, So, 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 . The angles are (y + 7) and (3y 17) In Exercises 9 and 10, trace \(\overline{A B}\). Copy and complete the following paragraph proof of the Alternate Interior Angles Converse using the diagram in Example 2. We know that, In geometry, there are three different types of lines, namely, parallel lines, perpendicular lines, and intersecting lines. -x = x 3 Perpendicular to \(y=\frac{1}{3}x+2\) and passing through \((4, 3)\). We can conclude that Click here for a Detailed Description of all the Parallel and Perpendicular Lines Worksheets. We can observe that 1 and 2 are the alternate exterior angles Find the slope of a line perpendicular to each given line. False, the letter A does not have a set of perpendicular lines because the intersecting lines do not meet each other at right angles. We can conclude that the distance of the gazebo from the nature trail is: 0.66 feet. It is given that the given angles are the alternate exterior angles So, We can conclude that Hence, from the above, The line through (k, 2) and (7, 0) is perpendicular to the line y = x \(\frac{28}{5}\). -2 = 3 (1) + c The equation that is perpendicular to y = -3 is: From the given figure, Answer: Perpendicular to \(y3=0\) and passing through \((6, 12)\). Compare the given points with b. 4 5, b. 3 (y 175) = x 50 = \(\sqrt{31.36 + 7.84}\) We know that, Question 22. 11y = 96 19 y = \(\frac{3}{2}\) d = \(\sqrt{(8 + 3) + (7 + 6)}\) So, y = -2x + c So, 2x + 4y = 4 Answer: Question 16. b = 9 1 = 60 These Parallel and Perpendicular Lines Worksheets are great for practicing identifying parallel, perpendicular, and intersecting lines from pictures. Answer: Hence, from the above, HOW DO YOU SEE IT? -x + 2y = 12 We know that, 1 = 32. Parallel to \(10x\frac{5}{7}y=12\) and passing through \((1, \frac{1}{2})\). PDF KM 654e-20150330181613 The points are: (-2, 3), (\(\frac{4}{5}\), \(\frac{13}{5}\)) In Exercises 7-10. find the value of x. A (-3, -2), and B (1, -2) = (\(\frac{-5 + 3}{2}\), \(\frac{-5 + 3}{2}\)) Converse: Hence, from the above, From the figure, Hence, d = 17.02 Hence, from the above figure, The product of the slopes of the perpendicular lines is equal to -1 a. m1 + m8 = 180 //From the given statement w y and z x Is your friend correct? Hence, They are not perpendicular because they are not intersecting at 90. x || y is proved by the Lines parallel to Transversal Theorem. We can observe that the given angles are corresponding angles = 3, The slope of line d (m) = \(\frac{y2 y1}{x2 x1}\) The best editor is directly at your fingertips offering you a range of advantageous instruments for submitting a Algebra 1 Worksheet 3 6 Parallel And Perpendicular Lines. Answer: If we keep in mind the geometric interpretation, then it will be easier to remember the process needed to solve the problem. c2= \(\frac{1}{2}\) From the given figure, x = \(\frac{69}{3}\) Where, the equation that is perpendicular to the given line equation is: If you even interchange the second and third statements, you could still prove the theorem as the second line before interchange is not necessary ABSTRACT REASONING The equation of the line that is parallel to the given equation is: 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. From the given figure, We can observe that, We know that, In this form, we see that perpendicular lines have slopes that are negative reciprocals, or opposite reciprocals. Answer: Question 21. From the given figure, Hence, from the above, By using the Alternate exterior angles Theorem, c = 2 It is given that 4 5. c1 = 4 XZ = \(\sqrt{(4 + 3) + (3 4)}\) y = x + 9 The given line has slope \(m=\frac{1}{4}\), and thus \(m_{}=+\frac{4}{1}=4\). We can conclude that the pair of perpendicular lines are: Two nonvertical lines in the same plane, with slopes \(m_{1}\) and \(m_{2}\), are perpendicular if the product of their slopes is \(1: m1m2=1\). The coordinates of line a are: (2, 2), and (-2, 3) It is given that If two lines are parallel to the same line, then they are parallel to each other Answer: 1 = 41 Question 47. The coordinates of P are (4, 4.5). Determine if the lines are parallel, perpendicular, or neither. REASONING The distance that the two of you walk together is: P = (7.8, 5) a.) We can observe that The lines containing the railings of the staircase, such as , are skew to all lines in the plane containing the ground. The given figure is: x1 = x2 = x3 . Answer: Using the properties of parallel and perpendicular lines, we can answer the given questions. Substitute A (3, -4) in the above equation to find the value of c We know that, = \(\sqrt{(9 3) + (9 3)}\) c = 7 The given equation is: -9 = 3 (-1) + c Answer: Perpendicular Lines Homework 5: Linear Equations Slope VIDEO ANSWER: Gone to find out which line is parallel, so we have for 2 parallel lines right. y = -2x + 2 Answer: There are many shapes around us that have parallel and perpendicular lines in them. We recognize that \(y=4\) is a horizontal line and we want to find a perpendicular line passing through \((3, 2)\). m = 2 The given equation is: We know that, Hence, Proof of the Converse of the Consecutive Interior angles Theorem: Explain your reasoning. The equation of the line that is parallel to the given line is: We can observe that (5y 21) = (6x + 32) Measure the lengths of the midpoint of AB i.e., AD and DB. 5 = -7 ( -1) + c b is the y-intercept Slope (m) = \(\frac{y2 y1}{x2 x1}\) CRITICAL THINKING which ones? Answer: 3 + 8 = 180 \(\overline{I J}\) and \(\overline{C D}\), c. a pair of paralIeI lines y = 3x 5 The product of the slopes of the perpendicular lines is equal to -1 y = -2x + 2. So, Repeat steps 3 and 4 below AB We can conclude that the value of x is: 14. c = 6 Hence, Answer: From the given figure, FSE = ESR 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. Write an equation of the line passing through the given point that is parallel to the given line. So, We can conclude that both converses are the same The given figure is: It can be observed that Substitute the given point in eq. We know that, m1m2 = -1 We know that, From the given figure, A bike path is being constructed perpendicular to Washington Boulevard through point P(2, 2). y = \(\frac{3}{2}\)x + 2, b. a. 4 6 = c We know that, Hence, Answer: These worksheets will produce 6 problems per page. A (x1, y1), and B (x2, y2) The equation of the line that is parallel to the given line equation is: a. y = 3x 6, Question 20. So, By using the consecutive interior angles theorem, = Undefined 5y = 116 + 21 y = x 3 The Parallel lines are the lines that do not intersect with each other and present in the same plane Hence, from the above, y = -7x + c y = \(\frac{1}{3}\)x + 10 Answer: 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. We know that, The points are: (-3, 7), (0, -2) It is given that m || n y = \(\frac{1}{3}\)x + \(\frac{26}{3}\) For the proofs of the theorems that you found to be true, refer to Exploration 1. m2 = -1 (2) y = -x + 1. Answer: It is not always the case that the given line is in slope-intercept form. The line parallel to \(\overline{Q R}\) is: \(\overline {L M}\), Question 3. Question 27. Parallel to \(y=\frac{1}{2}x+2\) and passing through \((6, 1)\). We know that, Hence, from the above, So, Determine the slope of a line parallel to \(y=5x+3\). = \(\frac{8 0}{1 + 7}\) For the intersection point of y = 2x, A Linear pair is a pair of adjacent angles formed when two lines intersect \(\frac{1}{2}\) . Writing Equations Of Parallel And Perpendicular Lines Answer Key Kuta Does either argument use correct reasoning? We know that, We can observe that Hence, Question 38. The representation of the given coordinate plane along with parallel lines is: c = -9 3 3. c = -2 y = -x + c Explain your reasoning. Draw \(\overline{A P}\) and construct an angle 1 on n at P so that PAB and 1 are corresponding angles The equation of a line is: = \(\frac{-3}{-1}\) From the given figure, Hence, Slope of line 1 = \(\frac{-2 1}{-7 + 3}\) PROBLEM-SOLVING The letter A has a set of perpendicular lines. We know that, The given table is: p || q and q || r. Find m8. A(2, 1), y = x + 4 Key Question: If x = 115, is it possible for y to equal 115? y = \(\frac{2}{3}\)x + c Answer: Write a conjecture about the resulting diagram. x = \(\frac{18}{2}\) Find the perpendicular line of y = 2x and find the intersection point of the two lines 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. 2x + 72 = 180 The slope of the given line is: m = 4 d = | x y + 4 | / \(\sqrt{2}\)} The lines that have the slopes product -1 and different y-intercepts are Perpendicular lines Note: Parallel lines are distinguished by a matching set of arrows on the lines that are parallel. Answer: Hence, from the above, What is the length of the field? We can conclude that the Corresponding Angles Converse is the converse of the Corresponding Angles Theorem, Question 3. We know that, What can you conclude? We know that, So, The parallel line equation that is parallel to the given equation is: So, Answer: 4x + 2y = 180(2) 42 and 6(2y 3) are the consecutive interior angles The given point is: (-5, 2) Using X as the center, open the compass so that it is greater than half of XP and draw an arc. 0 = \(\frac{5}{3}\) ( -8) + c Through the point \((6, 1)\) we found a parallel line, \(y=\frac{1}{2}x4\), shown dashed. When we compare the converses we obtained from the given statement and the actual converse, The given equation is: 1 + 2 = 180 Now, Parallel and Perpendicular Lines Perpendicular Lines Two nonvertical lines are perpendicular if their slopes are opposite reciprocals of each other. c = 1 The perpendicular line equation of y = 2x is: So, COMPLETE THE SENTENCE Explain your reasoning. 1 8, d. m6 + m ________ = 180 by the Consecutive Interior Angles Theorem (Thm. Is your friend correct? The given figure is: x = \(\frac{-6}{2}\) y = 2x + 3, Question 23. By comparing the given pair of lines with Determine which of the lines are parallel and which of the lines are perpendicular. y = -3x + c 1 Parallel And Perpendicular Lines Answer Key Pdf As recognized, adventure as without difficulty as experience just about lesson, amusement, as capably as harmony can be gotten by just checking out a Answer: Identify the slope and the y-intercept of the line. Answer: Linear Pair Perpendicular Theorem (Thm. So, To find the value of c, = Undefined Now, XY = 4.60 The equation that is perpendicular to the given line equation is: The slope of perpendicular lines is: -1 Hence, So, Answer: x = c Hence, We know that, Any fraction that contains 0 in the denominator has its value undefined a. Slope of the line (m) = \(\frac{y2 y1}{x2 x1}\) 1 and 3 are the corresponding angles, e. a pair of congruent alternate interior angles Yes, I support my friends claim, Explanation: Hence, We know that, We can say that any coincident line do not intersect at any point or intersect at 1 point From the given figure, x = 12 So, 2x + y = 162(1) The points are: (-9, -3), (-3, -9) We can conclude that a) Parallel to the given line: line(s) PerPendicular to . 2x + y = 0 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. The given figure is: We can conclude that the value of x when p || q is: 54, b. Hence, Now, \(\frac{1}{2}\) (m2) = -1 Now, Perpendicular lines have slopes that are opposite reciprocals, so remember to find the reciprocal and change the sign.