From the figure, Angles Theorem (Theorem 3.3) alike? y = mx + c The given coordinates are: A (1, 3), and B (8, 4) -5 8 = c The given point is: (-1, 6) Prove: l || m (1) and eq. We know that, The given line that is perpendicular to the given points is: P(- 7, 0), Q(1, 8) The given point is: (4, -5) WRITING We can conclude that the corresponding angles are: 1 and 5; 3 and 7; 2 and 4; 6 and 8, Question 8. Identifying Perpendicular Lines Worksheets 3 + 4 + 5 = 180 We know that, So, So, (1) = Eq. X (-3, 3), Y (3, 1) By comparing the given pair of lines with No, we did not name all the lines on the cube in parts (a) (c) except \(\overline{N Q}\). We can conclude that = \(\frac{4}{-18}\) Slope of AB = \(\frac{-4 2}{5 + 3}\) So, 2 = 140 (By using the Vertical angles theorem) 1. We have seen that the graph of a line is completely determined by two points or one point and its slope. Is she correct? Hence, from the above, In Exercise 31 on page 161, from the coordinate plane, From the coordinate plane, Draw \(\overline{A P}\) and construct an angle 1 on n at P so that PAB and 1 are corresponding angles Then explain how your diagram would need to change in order to prove that lines are parallel. So, Slope of TQ = \(\frac{-3}{-1}\) The slopes are equal fot the parallel lines What are Parallel and Perpendicular Lines? Answer: Write a conjecture about \(\overline{A B}\) and \(\overline{C D}\). Justify your answers. In Exercises 3 6, think of each segment in the diagram as part of a line. So, 2x = -6 c = \(\frac{37}{5}\) The coordinates of the line of the second equation are: (1, 0), and (0, -2) Line c and Line d are parallel lines Answer: Question 28. The conjectures about perpendicular lines are: 8 = 65 Hence, from the above, 1 8, d. m6 + m ________ = 180 by the Consecutive Interior Angles Theorem (Thm. c = 12 a is perpendicular to d and b isperpendicular to c, Question 22. Let A and B be two points on line m. Now, Select the angle that makes the statement true. Fro the given figure, how many right angles are formed by two perpendicular lines? Make the most out of these preparation resources and stand out from the rest of the crowd. 8 = 6 + b We know that, How are they different? We know that, We have to find the point of intersection Hence, from he above, We know that, Parallel lines are lines in the same plane that never intersect. We know that, We know that, = \(\frac{3}{4}\) 1 + 2 = 180 The lengths of the line segments are equal i.e., AO = OB and CO = OD. Find m1 and m2. Parallel & Perpendicular Lines Practice Answer Key Parallel and Perpendicular Lines Key *Note:If Google Docs displays "Sorry, we were unable to retrieve the document for viewing," refresh your browser. Given: m5 + m4 = 180 b) Perpendicular to the given line: In which of the following diagrams is \(\overline{A C}\) || \(\overline{B D}\) and \(\overline{A C}\) \(\overline{C D}\)? 1 = 180 57 Find the value of x when a b and b || c. Answer: Question 28. Because j K, j l What missing information is the student assuming from the diagram? -2 . In Exploration 2. m1 = 80. The given figure is: The Skew lines are the lines that are non-intersecting, non-parallel and non-coplanar a. So, y = -x + c Let the given points are: Maintaining Mathematical Proficiency Name them. We can conclude that 18 and 23 are the adjacent angles, c. We know that, (x1, y1), (x2, y2) We can conclude that 4 and 5 are the Vertical angles. 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. All the angle measures are equal If a || b and b || c, then a || c Alternate Interior Anglesare a pair ofangleson the inner side of each of those two lines but on opposite sides of the transversal. From the given figure, BCG and __________ are corresponding angles. Supply: lamborghini-islero.com During a game of pool. We know that, = (-1, -1) Thus the slope of any line parallel to the given line must be the same, \(m_{}=5\). Hence, x + 2y = 10 Now, We can conclude that 1 and 3 pair does not belong with the other three. We can observe that the product of the slopes are -1 and the y-intercepts are different Compare the given equation with S. Giveh the following information, determine which lines it any, are parallel. y = \(\frac{1}{2}\)x + 2 Check out the following pages related to parallel and perpendicular lines. By comparing the given pair of lines with x = 6, Question 8. The coordinates of line a are: (0, 2), and (-2, -2) Which angle pairs must be congruent for the lines to be parallel? So, A (x1, y1), and B (x2, y2) = 9.48 y = \(\frac{1}{2}\)x + 7 -(1) In a plane, if twolinesareperpendicularto the sameline, then they are parallel to each other. Linea and Line b are parallel lines Hence, Label points on the two creases. Answer: From the slopes, Answer: So, So, In Exercises 13 and 14, prove the theorem. The given statement is: Hence, from the above figure, Now, Hence, from the above, We know that, d = \(\sqrt{(x2 x1) + (y2 y1)}\) y = \(\frac{1}{2}\)x 7 The pair of lines that are different from the given pair of lines in Exploration 2 are: The map shows part of Denser, Colorado, Use the markings on the map. XY = 4.60 Hence, Identifying Parallel, Perpendicular, and Intersecting Lines from a Graph Apply slope formula, find whether the lines are parallel or perpendicular. So, We can observe that, Now, Answer: We know that, So, Likewise, parallel lines become perpendicular when one line is rotated 90. x = 180 73 a.) then they are parallel. From the given figure, Perpendicular to \(y3=0\) and passing through \((6, 12)\). 2 = \(\frac{1}{2}\) (-5) + c Chapter 3 Parallel and Perpendicular Lines Key. Prove c||d We can conclude that the value of x when p || q is: 54, b. Now, Enter a statement or reason in each blank to complete the two-column proof. Answer: Question 38. We can conclude that if you use the third statement before the second statement, you could still prove the theorem, Question 4. EG = 7.07 The general steps for finding the equation of a line are outlined in the following example. y = x + 4 We can conclude that the value of XZ is: 7.07, Find the length of \(\overline{X Y}\) We can conclude that Now, m1 and m5 So, Using the same compass selling, draw an arc with center B on each side \(\overline{A B}\). Answer: Write an inequality for the slope of a line perpendicular to l. Explain your reasoning. m2 = \(\frac{1}{2}\) So, The perpendicular line equation of y = 2x is: line(s) skew to . The equation of the parallel line that passes through (1, 5) is y = -7x 2. y = \(\frac{3}{2}\)x + 2 For example, if the equation of two lines is given as, y = 4x + 3 and y = 4x - 5, we can see that their slope is equal (4). The representation of the parallel lines in the coordinate plane is: In Exercises 17 20. write an equation of the line passing through point P that is perpendicular to the given line. Given: 1 2 Hence, from the above, Hence, We can conclude that the converse we obtained from the given statement is true 5-6 parallel and perpendicular lines, so we're still dealing with y is equal to MX plus B remember that M is our slope, so that's what we're going to be working with a lot today we have parallel and perpendicular lines so parallel these lines never cross and how they're never going to cross it because they have the same slope an example would be to have 2x plus 4 or 2x minus 3, so we see the 2 . Answer: WRITING Describe and correct the error in the students reasoning x = n We can observe that the given lines are parallel lines The given equation is: Let's expand 2 (x 5) and then rearrange: y 4 = 2x 10. if two lines are perpendicular to the same line. y = mx + c Two lines, a and b, are perpendicular to line c. Line d is parallel to line c. The distance between lines a and b is x meters. Hence, from the above, 68 + (2x + 4) = 180 2 and 3 are the consecutive interior angles The given figure is: We can conclude that 1 = 2 = 150, Question 6. The given figure is: Hence, from the above, We can conclude that y = \(\frac{2}{3}\)x + 9, Question 10. Label the point of intersection as Z. Parallel and perpendicular lines worksheet answers key geometry - Note: This worksheet is supported by a flash presentation, under Mausmi's Math Q2: Determine. In diagram. E (-4, -3), G (1, 2) We know that, Now, The equation that is perpendicular to the given line equation is: So, Question 5. Unit 3 (Parallel & Perpendicular Lines) In this unit, you will: Identify parallel and perpendicular lines Identify angle relationships formed by a transversal Solve for missing angles using angle relationships Prove lines are parallel using converse postulate and theorems Determine the slope of parallel and perpendicular lines Write and graph So, Perpendicular lines are lines in the same plane that intersect at right angles (\(90\) degrees). Substitute (1, -2) in the above equation The angles that are opposite to each other when 2 lines cross are called Vertical angles We can conclude that we can use Perpendicular Postulate to show that \(\overline{A C}\) is not perpendicular to \(\overline{B F}\), Question 3. 3. Now, Answer: Is your friend correct? The given figure is: Point A is perpendicular to Point C We can say that all the angle measures are equal in Exploration 1 d = \(\sqrt{(x2 x1) + (y2 y1)}\) (2x + 15) = 135 a. Hence, Answer: Hence, from the above, 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. Perpendicular to \(x+7=0\) and passing through \((5, 10)\). Hence, from the above, The product of the slopes is -1 and the y-intercepts are different Answer: x + 2y = -2 Answer: d = \(\sqrt{(11) + (13)}\) From the given figure, The slopes are the same and the y-intercepts are different BCG and __________ are consecutive interior angles. Answer: Question 2. Now, Write an equation for a line parallel to y = 1/3x - 3 through (4, 4) Q. = \(\sqrt{(250 300) + (150 400)}\) So, Hence, from the above figure, Answer: Question 32. The equation of the line along with y-intercept is: y = mx + c From the given figure, Substitute the given point in eq. Now, Answer: The given figure is: Identify all the pairs of vertical angles. A(3, 4),y = x + 8 Answer: b is the y-intercept We can conclude that the pair of parallel lines are: So, y = mx + c Write an equation for a line perpendicular to y = -5x + 3 through (-5, -4) (2, 7); 5 1 2 11 Download Parallel and Perpendicular Lines Worksheet - Mausmi Jadhav. Now, P(0, 1), y = 2x + 3 Use the theorems from Section 3.2 and the converses of those theorems in this section to write three biconditional statements about parallel lines and transversals. The midpoint of PQ = (\(\frac{x1 + x2}{2}\), \(\frac{y1 + y2}{2}\)) To find the coordinates of P, add slope to AP and PB Substitute (-1, -9) in the given equation Now, We know that, y = 2x If you will go to the park, then it is warm outside -> False. The LibreTexts libraries arePowered by NICE CXone Expertand are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. So, The equation that is parallel to the given equation is: The equation for another line is: In Exercises 21 and 22, write and solve a system of linear equations to find the values of x and y. x = \(\frac{87}{6}\) If two parallel lines are cut by a transversal, then the pairs of Alternate exterior angles are congruent. We can conclude that b || a, Question 4. Answer: Answer: Now, 3m2 = -1 We use this and the point \((\frac{7}{2}, 1)\) in point-slope form. y = \(\frac{2}{3}\)x + b (1) XY = \(\sqrt{(3 + 1.5) + (3 2)}\) c = -2 Now, In the diagram below. A (x1, y1), B (x2, y2) m1 = 76 The perpendicular equation of y = 2x is: so they cannot be on the same plane. We can conclude that the slope of the given line is: \(\frac{-3}{4}\), Question 2. Answer: We get Use these steps to prove the Transitive Property of Parallel Lines Theorem x = \(\frac{84}{7}\) Question 17. Explain your reasoning? y = \(\frac{1}{5}\) (x + 4) (B) intersect From the given figure, Algebra 1 worksheet 36 parallel and perpendicular lines answer key. We can conclude that \(\overline{N P}\) and \(\overline{P O}\) are perpendicular lines, Question 10. So, We know that, = \(\frac{6}{2}\) corresponding The slope of line a (m) = \(\frac{y2 y1}{x2 x1}\) m = \(\frac{0 + 3}{0 1.5}\) We know that, Question 41. The slope of the parallel line that passes through (1, 5) is: 3 Which theorems allow you to conclude that m || n? d = | 6 4 + 4 |/ \(\sqrt{2}\)} Hence, from the above, Now, So, Compare the given coordinates with (x1, y1), and (x2, y2) We can observe that a is perpendicular to both the lines b and c The given figure is: The distance wont be in negative value, m2 = 2 y = \(\frac{1}{3}\)x + 10 = 5.70 The Skew lines are the lines that are not parallel, non-intersect, and non-coplanar A (-1, 2), and B (3, -1) Now, y = -x + c The slopes of the parallel lines are the same We have to prove that m || n A (x1, y1), B (x2, y2) So, The point of intersection = (\(\frac{7}{2}\), \(\frac{1}{2}\)) Hence, from the above, Question 22. Question 3. The product of the slopes of the perpendicular lines is equal to -1 Compare the given equation with 7x = 84 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. Hence, from the above, Question 11. So, So, Answer: Answer: The lines that do not have any intersection points are called Parallel lines The give pair of lines are: Determine which lines, if any, must be parallel. (0, 9); m = \(\frac{2}{3}\) To be proficient in math, you need to understand and use stated assumptions, definitions, and previously established results. y = \(\frac{137}{5}\) 1 = 3 (By using the Corresponding angles theorem) Question 2. It is given that 1 = 58 A hand rail is put in alongside the steps of a brand new home as proven within the determine. We can conclude that quadrilateral JKLM is a square. Hence, it can be said that if the slope of two lines is the same, they are identified as parallel lines, whereas, if the slope of two given lines are negative reciprocals of each other, they are identified as perpendicular lines. We can conclude that Answer: So, 1 4. So, No, your friend is not correct, Explanation: The given figure is: The given point is: A (8, 2) The Parallel lines are the lines that do not intersect with each other and present in the same plane Hence, 9 0 = b Through the point \((6, 1)\) we found a parallel line, \(y=\frac{1}{2}x4\), shown dashed. So, PROVING A THEOREM The equation of the line that is perpendicular to the given line equation is: Hence, from the above, So, y = -2x 2 2x x = 56 2 We can conclude that the tallest bar is parallel to the shortest bar, b. a. The conjecture about \(\overline{A B}\) and \(\overline{c D}\) is: Which values of a and b will ensure that the sides of the finished frame are parallel.? 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 \(1\). (-3, 8); m = 2 Hence, from the above, Hence, The vertical angles are congruent i.e., the angle measures of the vertical angles are equal We can observe that the length of all the line segments are equal a. 0 = 3 (2) + c 6-3 Write Equations of Parallel and Perpendicular Lines Worksheet. Prove \(\overline{A B} \| \overline{C D}\) y = -2x + 8 Now, First, solve for \(y\) and express the line in slope-intercept form. We know that, From the given figure, i.e., Justify your answer. then the pairs of consecutive interior angles are supplementary. Find the equation of the line passing through \((8, 2)\) and perpendicular to \(6x+3y=1\). Answer: The angles that have the opposite corners are called Vertical angles 2 and 4 are the alternate interior angles We know that, Slope of line 1 = \(\frac{9 5}{-8 10}\) Converse: The two pairs of supplementary angles when \(\overline{A B}\) and \(\overline{D C}\) are parallel is: ACD and BDC. Answer: Question 9. y 3y = -17 7 So, The standard form of a linear equation is: Determine whether the converse is true. According to Corresponding Angles Theorem, From the given figure, Now, If the slope of two given lines are negative reciprocals of each other, they are identified as perpendicular lines. c. m5=m1 // (1), (2), transitive property of equality On the other hand, when two lines intersect each other at an angle of 90, they are known as perpendicular lines. Now, Answer: c = -2 -x x = -3 Hence, (5y 21) = 116 Answer: Identify two pairs of perpendicular lines. The given points are: Describe and correct the error in determining whether the lines are parallel. = 0 180 = x + x The coordinates of line c are: (2, 4), and (0, -2) c. y = 5x + 6 So, Hence, from the above, Find the distance from point X to Parallel and Perpendicular Lines Perpendicular Lines Two nonvertical lines are perpendicular if their slopes are opposite reciprocals of each other. Write an equation of the line that passes through the given point and has the given slope. y1 = y2 = y3 Now, Hence, All its angles are right angles. To find the value of c, Compare the given equation with The coordinates of the meeting point are: (150, 200) The given figure is: So, y = \(\frac{156}{12}\) The alternate exterior angles are: 1 and 7; 6 and 4, d. consecutive interior angles We can conclude that the distance of the gazebo from the nature trail is: 0.66 feet. 4.7 of 5 (20 votes) Fill PDF Online Download PDF. ANALYZING RELATIONSHIPS For example, if the equations of two lines are given as: y = 1/4x + 3 and y = - 4x + 2, we can see that the slope of one line is the negative reciprocal of the other. Suppose point P divides the directed line segment XY So that the ratio 0f XP to PY is 3 to 5. Hence, y = \(\frac{7}{2}\) 3 We know that, y = -2x + 1 The given figure is: Answer: Question 32. Question 42. Embedded mathematical practices, exercises provided make it easy for you to understand the concepts quite quickly. -2y = -24 We can also observe that w and z is not both to x and y b. m1 + m4 = 180 // Linear pair of angles are supplementary So, So, They are always the same distance apart and are equidistant lines. The product of the slopes of the perpendicular lines is equal to -1 \(\begin{aligned} 6x+3y&=1 \\ 6x+3y\color{Cerulean}{-6x}&=1\color{Cerulean}{-6x} \\ 3y&=-6x+1 \\ \frac{3y}{\color{Cerulean}{3}}&=\frac{-6x+1}{\color{Cerulean}{3}} \\ y&=\frac{-6x}{3}+\frac{1}{3}\\y&=-2x+\frac{1}{3} \end{aligned}\). Compare the given points with -5 2 = b a. m5 + m4 = 180 //From the given statement Find the equation of the line perpendicular to \(x3y=9\) and passing through \((\frac{1}{2}, 2)\). c = 4 3 We can conclude that the equation of the line that is perpendicular bisector is: = \(\frac{1}{3}\) The slope of line l is greater than 0 and less than 1. The midpoint of PQ = (\(\frac{x1 + x2}{2}\), \(\frac{y1 + y2}{2}\)) The equation that is perpendicular to the given line equation is: b = -5 Hence, Hence, from the above, We can observe that 3.4). From the given figure, 140 21 32 = 6x To find the value of c, The coordinates of the midpoint of the line segment joining the two houses = (150, 250) The points are: (3, 4), (\(\frac{3}{2}\), \(\frac{3}{2}\)) as corresponding angles formed by a transversal of parallel lines, and so, WRITING 1 = 40 and 2 = 140. Answer: AP : PB = 2 : 6 Answer: When finding an equation of a line perpendicular to a horizontal or vertical line, it is best to consider the geometric interpretation. The lines that do not intersect and are not parallel and are not coplanar are Skew lines Yes, there is enough information in the diagram to conclude m || n. Explanation: The given table is: perpendicular lines. The Coincident lines may be intersecting or parallel Compare the given equation with The given point is: (6, 4) According to the Perpendicular Transversal theorem, Use the diagram. x = y =29 Is it possible for all eight angles formed to have the same measure? Now, 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? The representation of the given pair of lines in the coordinate plane is: The given lines are perpendicular lines In Exercises 3-6, find m1 and m2. To find the distance from point X to \(\overline{W Z}\), c = \(\frac{9}{2}\) \(\overline{D H}\) and \(\overline{F G}\) Question 5. Explain. We know that, x = y = 29, Question 8. (C) Alternate Exterior Angles Converse (Thm 3.7) \(\overline{I J}\) and \(\overline{C D}\), c. a pair of paralIeI lines d = \(\sqrt{(x2 x1) + (y2 y1)}\) The given coordinates are: A (-3, 2), and B (5, -4) Answer: Which rays are parallel? Answer: 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. We can conclude that the parallel lines are: m = -7 Corresponding Angles Theorem (Theorem 3.1): If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. Homework 1 - State whether the given pair of lines are parallel. By using the corresponding angles theorem, Label the intersections as points X and Y. So, Perpendicular lines are those that always intersect each other at right angles. So, m1m2 = -1 y = \(\frac{1}{3}\)x + \(\frac{475}{3}\) The given figure is: Question 47. y = -3 6 Answer Keys - These are for all the unlocked materials above. Answer: We can conclude that m || n, Question 15. Hence, from the above, Hence, The given points are: A (x1, y1), and B (x2, y2) In Exercises 11 and 12. find m1, m2, and m3. Answer: From the given figure, Answer: The postulates and theorems in this book represent Euclidean geometry. y = \(\frac{1}{5}\)x + \(\frac{37}{5}\) Draw \(\overline{P Z}\), CONSTRUCTION The given equation is: The "Parallel and Perpendicular Lines Worksheet (+Answer Key)" can help you learn about the different properties and theorems of parallel and perpendicular lines. m1 m2 = -1 (2) So, by the Corresponding Angles Converse, g || h. Question 5. The product of the slopes is -1 The given figure shows that angles 1 and 2 are Consecutive Interior angles The product of the slopes of the perpendicular lines is equal to -1 When we compare the given equation with the obtained equation, According to the Alternate Interior Angles Theorem, the alternate interior angles are congruent Hence, MAKING AN ARGUMENT So, The slope of the given line is: m = -2 Parallel and Perpendicular Lines From the given slopes of the lines, identify whether the two lines are parallel, perpendicular, or neither. Write a conjecture about \(\overline{A O}\) and \(\overline{O B}\) Justify your conjecture. We know that, Homework 2 - State whether the given pair are parallel, perpendicular, or intersecting. From the figure, Now, The product of the slopes of the perpendicular lines is equal to -1 With Cuemath, you will learn visually and be surprised by the outcomes. A coordinate plane has been superimposed on a diagram of the football field where 1 unit = 20 feet. = -3 By using the Corresponding angles Theorem, y = \(\frac{3}{2}\) + 4 and -3x + 2y = -1 From the above figure, Hence, from the above, (7x + 24) = 108 From the figure, Our Parallel and Perpendicular Lines Worksheets are free to download, easy to use, and very flexible. a. 17x + 27 = 180 Since it must pass through \((3, 2)\), we conclude that \(x=3\) is the equation. Fold the paper again so that point A coincides with point B. Crease the paper on that fold. b. y = \(\frac{1}{2}\)x 2 Now, ANALYZING RELATIONSHIPS We can say that w and v are parallel lines by Perpendicular Transversal Theorem We can observe that the sum of the angle measures of all the pairs i.e., (115 + 65), (115 + 65), and (65 + 65) is not 180 Now, Answer: Now, Answer: a. m5 + m4 = 180 //From the given statement The distance from the point (x, y) to the line ax + by + c = 0 is: Justify your conjecture. From the given figure, The standard form of the equation is: The parallel line equation that is parallel to the given equation is: Explain your reasoning. Cops the diagram with the Transitive Property of Parallel Lines Theorem on page 141. Answer: Question 22. To be proficient in math, you need to make conjectures and build a logical progression of statements to explore the truth of your conjectures. The angles that have the common side are called Adjacent angles a. Each bar is parallel to the bar directly next to it. Find the measures of the eight angles that are formed. y 500 = -3x + 150 The equation of the line that is perpendicular to the given equation is: The letter A has a set of perpendicular lines. y = \(\frac{1}{3}\) (10) 4 Perpendicular to \(y=x\) and passing through \((7, 13)\). Which lines are parallel to ? In Exercises 9 and 10, use a compass and straightedge to construct a line through point P that is parallel to line m. Question 10. The representation of the Converse of the Consecutive Interior angles Theorem is: Question 2. (1) Given Slope of a Line Find Slopes for Parallel and Perpendicular Lines Worksheets We know that, It also shows that a and b are cut by a transversal and they have the same length Parallel Curves (4.3.1) - Parallel and Perpendicular Lines Parallel lines have the same slope and different y- intercepts. So, Hence, Answer: Question 30. = \(\sqrt{2500 + 62,500}\) z x and w z y = -2x + \(\frac{9}{2}\) (2) Answer: line(s) parallel to transv. m1m2 = -1 Hence, from the above, 0 = \(\frac{1}{2}\) (4) + c Compare the given points with y = mx + c So, Now, Hence, from the above, = 920 feet 1 = 40 From the converse of the Consecutive Interior angles Theorem, According to the Vertical Angles Theorem, the vertical angles are congruent = 180 76 y = \(\frac{1}{3}\)x + \(\frac{16}{3}\), Question 5. Answer: 35 + y = 180 y = \(\frac{1}{2}\)x + c a.) Hence, from the above, 1 = 0 + c Answer: Question 24. So, Hence, So, Explain your reasoning. (2) to get the values of x and y (A) Corresponding Angles Converse (Thm 3.5) c.) Book: The two highlighted lines meet each other at 90, therefore, they are perpendicular lines. Hence, from the above, Two lines that do not intersect and are also not parallel are ________ lines. Question 39. The standard form of the equation is: The given perpendicular line equations are: The distance between the two parallel lines is: We can observe that y = -2x 1 (2) d = \(\sqrt{(x2 x1) + (y2 y1)}\) Explain why the top rung is parallel to the bottom rung. The given equation in the slope-intercept form is: In this form, we see that perpendicular lines have slopes that are negative reciprocals, or opposite reciprocals. Hence, from the above, Corresponding Angles Theorem This contradicts what was given,that angles 1 and 2 are congruent. Hence, The measure of 1 is 70. We get, x = 147 14 It is given that m || n We can conclude that the line parallel to \(\overline{N Q}\) is: \(\overline{M P}\), b. So, Are the markings on the diagram enough to conclude that any lines are parallel? x 2y = 2 We can conclude that the lines x = 4 and y = 2 are perpendicular lines, Question 6. y = x + 9 We know that, Hence, from the above, The slopes of perpendicular lines are undefined and 0 respectively EG = \(\sqrt{(5) + (5)}\) MODELING WITH MATHEMATICS The equation that is perpendicular to the given line equation is: Answer: We can observe that the slopes are the same and the y-intercepts are different Hence, from the above, 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 b. 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 The representation of the given pair of lines in the coordinate plane is: Substitute P (3, 8) in the above equation to find the value of c m2 = 1 The coordinates of line 2 are: (2, -1), (8, 4) 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. Answer: So, So, (5y 21) = (6x + 32) Using the properties of parallel and perpendicular lines, we can answer the given questions. What conjectures can you make about perpendicular lines? = \(\frac{15}{45}\) Hence, from the above, Answer: Question 12. Q. y = \(\frac{1}{6}\)x 8 We can observe that We can conclude that These Parallel and Perpendicular Lines Worksheets will give the slopes of two lines and ask the student if the lines are parallel, perpendicular, or neither. It is given that, 61 and y are the alternate interior angles Hence, from the above, Hence, from the above figure, Two lines are cut by a transversal. So, 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). Given: k || l So, We know that,