The equation for another line is: Answer: The given point is: A (-9, -3) Draw an arc with center A on each side of AB. Hence, from the above, Question 12. So, 3. The given point is: A (0, 3) y = 2x + c The angles that are opposite to each other when two lines cross are called Vertical angles a. The lines that do not intersect and are not parallel and are not coplanar are Skew lines The slopes are equal for the parallel lines It is given that in spherical geometry, all points are points on the surface of a sphere. Hence, from the above, All ordered pair solutions of a vertical line must share the same \(x\)-coordinate. The standard form of the equation is: The equation of a straight line is represented as y = ax + b which defines the slope and the y-intercept. Hence, from the above, Answer: Question 26. b. m1 + m4 = 180 // Linear pair of angles are supplementary For a pair of lines to be non-perpendicular, the product of the slopes i.e., the product of the slope of the first line and the slope of the second line will not be equal to -1 Answer: Question 36. Hence, Hence, from the above, Answer: c is the y-intercept a. Question 27. Use the Distance Formula to find the distance between the two points. Do you support your friends claim? which ones? Find the distance front point A to the given line. Get Algebra 1 Worksheet 3 6 Parallel And Perpendicular Lines What is the distance between the lines y = 2x and y = 2x + 5? x + 2y = 10 a. Art and Culture: Abstract Art: Lines, Rays, and Angles - Saskia Lacey 2017-09-01 Students will develop their geometry skills as they study the geometric shapes of modern art and read about the . Q (2, 6), R (6, 4), S (5, 1), and T (1, 3) Definition of Parallel and Perpendicular Parallel lines are lines in the same plane that never intersect. Answer: A (x1, y1), B (x2, y2) 2 = 2 (-5) + c We can conclude that the value of XZ is: 7.07, Find the length of \(\overline{X Y}\) We know that, Is your friend correct? This can be proven by following the below steps: 3x 5y = 6 The equation of line p is: 1 = 53.7 and 5 = 53.7 Hence, from the above, Sandwich: The highlighted lines in the sandwich are neither parallel nor perpendicular lines. \(m_{}=4\) and \(m_{}=\frac{1}{4}\), 5. We can conclude that The given figure is: Answer: It is given that Step 1: Find the slope \(m\). Answer: Answer: Question 38. Compare the given equation with d = \(\sqrt{(13 9) + (1 + 4)}\) Equations of Parallel and Perpendicular Lines - ChiliMath Students must unlock 5 locks by: 1: determining if two given slopes are parallel, perpendicular or neither. y = \(\frac{1}{2}\)x 6 These worksheets will produce 10 problems per page. y = 4x + 9, Question 7. The Coincident lines are the lines that lie on one another and in the same plane Write an inequality for the slope of a line perpendicular to l. Explain your reasoning. 9 = 0 + b To find the value of b, = 9.48 Geometry parallel and perpendicular lines answer key Find the slope of a line perpendicular to each given line. 3 = 2 (-2) + x 4 ________ b the Alternate Interior Angles Theorem (Thm. You and your mom visit the shopping mall while your dad and your sister visit the aquarium. y = 3x + c The given point is: A (3, 4) The given figure is: The given equation is: We know that, So, For a parallel line, there will be no intersecting point 3 = 47 BCG and __________ are corresponding angles. Decide whether there is enough information to prove that m || n. If so, state the theorem you would use. Hence, We can conclude that the pair of parallel lines are: Question 37. Given a b P(4, 6)y = 3 The slopes are equal fot the parallel lines 5 = 105, To find 8: Now, y1 = y2 = y3 So, We can observe that 3 and 8 are consecutive exterior angles. MAKING AN ARGUMENT y = -2 (-1) + \(\frac{9}{2}\) b = 9 = \(\frac{325 175}{500 50}\) Hence, From the above figure, transv. We know that, Hence, from he above, The given figure is: Therefore, they are parallel lines. So, Slope of AB = \(\frac{5 1}{4 + 2}\) The intersecting lines intersect each other and have different slopes and have the same y-intercept a. y = 4x + 9 Answer: Answer: The coordinates of line p are: So, In a plane, if a line is perpendicular to one of two parallellines, then it is perpendicular to the other line also. 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 equation for another perpendicular line is: Then write So, We can conclude that the consecutive interior angles of BCG are: FCA and BCA. x = \(\frac{4}{5}\) Using Y as the center and retaining the same compass setting, draw an arc that intersects with the first Supply: lamborghini-islero.com So, -5 2 = b a. 5 + 4 = b Parallel lines are those lines that do not intersect at all and are always the same distance apart. Draw a diagram of at least two lines cut by at least one transversal. We can conclude that the value of x when p || q is: 54, b. The converse of the Alternate Interior angles Theorem: We can say that any parallel line do not intersect at any point So, 3.6 Slopes of Parallel and Perpendicular Lines - GEOMETRY y = \(\frac{2}{3}\)x + 1 By using the Corresponding Angles Theorem, The given point is: A (-2, 3) The equation that is perpendicular to the given line equation is: ID Unit 3: Paraliel& Perpendicular Lines Homework 3: | Chegg.com A triangle has vertices L(0, 6), M(5, 8). The given equation is: We can conclude that the perpendicular lines are: The Converse of the alternate exterior angles Theorem: The converse of the given statement is: By comparing the slopes, Now, 3y = x 50 + 525 Answer: Question 14. Perpendicular lines are denoted by the symbol . m1m2 = -1 Hence, Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 3y 525 = x 50 The equation of the perpendicular line that passes through (1, 5) is: If two parallel lines are cut by a transversal, then the pairs of Alternate interior angles are congruent. Slope of ST = \(\frac{1}{2}\), Slope of TQ = \(\frac{3 6}{1 2}\) Answer: Question 52. = \(\frac{2}{9}\) From the figure, y = \(\frac{1}{2}\)x + 6 Hence, from the above, So, Answer: Answer: Hence, from the above, 3 = 2 ( 0) + c You decide to meet at the intersection of lines q and p. Each unit in the coordinate plane corresponds to 50 yards. Identifying Parallel, Perpendicular, and Intersecting Lines Worksheets Hence, from the above, 2y + 4x = 180 By using the linear pair theorem, We know that, c = 7 To find the distance from line l to point X, Answer: Question 44. The lines that have the same slope and different y-intercepts are Parallel lines = 104 Your school is installing new turf on the football held. Linear Pair Perpendicular Theorem (Thm. We can conclude that 75 and 75 are alternate interior angles, d. The slope of the given line is: m = -2 The slope of perpendicular lines is: -1 \(\overline{C D}\) and \(\overline{A E}\) Substitute (-1, -9) in the given equation XY = 6.32 The two lines are Intersecting when they intersect each other and are coplanar By using the Vertical Angles Theorem, x = 35 and y = 145, Question 6. (-3, 7), and (8, -6) y = 12 We know that, x = 9 The Skew lines are the lines that are non-intersecting, non-parallel and non-coplanar Verify your answer. To find the distance between the two lines, we have to find the intersection point of the line Now, The lines that have the slopes product -1 and different y-intercepts are Perpendicular lines We know that, Two lines are termed as parallel if they lie in the same plane, are the same distance apart, and never meet each other. Hence, From the given figure, Question 39. Question 25. In Exercise 31 on page 161, from the coordinate plane, Hence, Now, Answer: If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent Answer: = \(\sqrt{(3 / 2) + (3 / 2)}\) From the above, From the coordinate plane, y = -2x + 2 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). Answer: What shape is formed by the intersections of the four lines? Once the equation is already in the slope intercept form, you can immediately identify the slope. y = mx + c 0 = \(\frac{5}{3}\) ( -8) + c Inverses Tables Table of contents Parallel Lines Example 2 Example 3 Perpendicular Lines Example 1 Example 2 Example 3 Interactive From the given figure, y = \(\frac{7}{2}\) 3 You and your family are visiting some attractions while on vacation. We know that, construction change if you were to construct a rectangle? Now, So, Is it possible for consecutive interior angles to be congruent? From the given figure, 8x = 42 2 So, = \(\frac{2}{9}\) A(-1, 5), y = \(\frac{1}{7}\)x + 4 Question 11. So, The general steps for finding the equation of a line are outlined in the following example. y = 180 35 Prove the statement: If two lines are horizontal, then they are parallel. m2 = -1 ABSTRACT REASONING d = \(\sqrt{(300 200) + (500 150)}\) Hence, from the above, We can conclude that the distance from line l to point X is: 6.32. Justify your answer for cacti angle measure. 1 = -3 (6) + b 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 2 ________ by the Corresponding Angles Theorem (Thm. Point A is perpendicular to Point C b. Alternate Exterior angles Theorem 3 = 68 and 8 = (2x + 4) Determine the slope of a line perpendicular to \(3x7y=21\). = \(\frac{50 500}{200 50}\) So, For perpendicular lines, .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. y = \(\frac{137}{5}\) We know that, y = -3 (0) 2 Hence, So, The equation that is parallel to the given equation is: y = \(\frac{3}{2}\)x 1 Find the slope of the line perpendicular to \(15x+5y=20\). We can conclude that PDF ANSWERS Answer: y = mx + c Repeat steps 3 and 4 below AB x = \(\frac{40}{8}\) So, Substitute the given point in eq. PROVING A THEOREM From the given figure, Hence, from the above figure, From the given figure, The coordinates of the line of the first equation are: (-1.5, 0), and (0, 3) We can observe that there are 2 perpendicular lines So, MODELING WITH MATHEMATICS The lines skew to \(\overline{Q R}\) are: \(\overline{J N}\), \(\overline{J K}\), \(\overline{K L}\), and \(\overline{L M}\), Question 4. According to the Alternate Interior Angles theorem, the alternate interior angles are congruent (50, 175), (500, 325) y = \(\frac{1}{2}\)x + 5 We know that, The equation of a line is: Compare the given equation with Let the congruent angle be P Answer: d. AB||CD // Converse of the Corresponding Angles Theorem The given point is: A (-6, 5) We can conclude that the distance from point A to the given line is: 6.26. c = \(\frac{1}{2}\) c = 5 + \(\frac{1}{3}\) Substitute (0, -2) in the above equation Lets draw that line, and call it P. Lets also call the angle formed by the traversal line and this new line angle 3, and we see that if we add some other angle, call it angle 4, to it, it will be the same as angle 2. Answer: Answer: You can select different variables to customize these Parallel and Perpendicular Lines Worksheets for your needs. a. PROOF Slope (m) = \(\frac{y2 y1}{x2 x1}\) This contradiction means our assumption (L1 is not parallel to L2) is false, and so L1 must be parallel to L2. a. m5 + m4 = 180 //From the given statement c = -1 2 PROVING A THEOREM 5 = \(\frac{1}{3}\) + c your friend claims to be able to make the shot Shown in the diagram by hitting the cue ball so that m1 = 25. m = \(\frac{3}{-1.5}\) y = \(\frac{8}{5}\) 1 Hence, from the above, y = \(\frac{1}{2}\)x + 8, Question 19. Hence, So, First, find the slope of the given line. The equation of the perpendicular line that passes through (1, 5) is: x + 2y = 2 From the given figure, Answer: y = \(\frac{2}{3}\) From ESR, Now, Answer: = \(\frac{1}{4}\), The slope of line b (m) = \(\frac{y2 y1}{x2 x1}\) The parallel line equation that is parallel to the given equation is: In a plane, if a line is perpendicular to one of two parallellines, then it is perpendicular to the other line also. m1m2 = -1 The given figure is: So, Hence, from the above, Intersecting lines share exactly one point that is where they meet each other, which is called the point of intersection. y = -2x 1 (2) Geometrically, we see that the line \(y=4x1\), shown dashed below, passes through \((1, 5)\) and is perpendicular to the given line. y = -2x + 8 5 = c The product of the slopes of the perpendicular lines is equal to -1 Question 3. y = \(\frac{1}{2}\)x + c Newest Parallel And Perpendicular Lines Questions - Wyzant Answer: Question 34. C(5, 0) According to the Corresponding Angles Theorem, the corresponding angles are congruent We can conclude that we can not find the distance between any two parallel lines if a point and a line is given to find the distance, Question 2. Select all that apply. y = \(\frac{1}{3}\)x 2. The Converse of the Alternate Exterior Angles Theorem: c = -4 + 3 We can conclude that the slope of the given line is: 3, Question 3. y = \(\frac{1}{2}\)x + c 1 = 80 PROBLEM-SOLVING (6, 22); y523 x1 4 13. The equation that is perpendicular to the given line equation is: Let's try the best Geometry chapter 3 parallel and perpendicular lines answer key. Hence, 4.5 Equations of Parallel and Perpendicular Lines Solving word questions The alternate interior angles are: 3 and 5; 2 and 8, c. alternate exterior angles y = -x + c In Exercises 7-10. find the value of x. So, A line is a circle on the sphere whose diameter is equal to the diameter of the sphere. (2x + 15) = 135 line(s) perpendicular to We know that, 5y = 3x 6 Hence, from the above, Answer: Identify the slope and the y-intercept of the line. Proof: Given 1 2, 3 4 1 = 4 The given figure is: Answer: y = \(\frac{1}{2}\)x 2 Similarly, observe the intersecting lines in the letters L and T that have perpendicular lines in them. Measure the lengths of the midpoint of AB i.e., AD and DB. We can observe that Now, 2 = 150 (By using the Alternate exterior angles theorem) (2) to get the values of x and y The parallel line equation that is parallel to the given equation is: P(0, 0), y = 9x 1 Substitute this slope and the given point into point-slope form. REASONING The points are: (2, -1), (\(\frac{7}{2}\), \(\frac{1}{2}\)) We can observe that the given angles are the corresponding angles We can conclude that the value of x is: 54, Question 3. We can observe that Answer: Answer: Which pair of angle measures does not belong with the other three? We know that, Answer: (x1, y1), (x2, y2) A(- 6, 5), y = \(\frac{1}{2}\)x 7 To find the value of c, Answer: a. y = -2x 2, f. c = -3 + 4 Let's expand 2 (x 5) and then rearrange: y 4 = 2x 10. No, the third line does not necessarily be a transversal, Explanation: The portion of the diagram that you used to answer Exercise 26 on page 130 is: Question 2. So, A(1, 6), B(- 2, 3); 5 to 1 Explain your reasoning. The lines containing the railings of the staircase, such as , are skew to all lines in the plane containing the ground. Hence, from the above, It is given that the sides of the angled support are parallel and the support makes a 32 angle with the floor (1) Answer: We know that, Answer: Slope (m) = \(\frac{y2 y1}{x2 x1}\) Explain. The line that is perpendicular to y=n is: (13, 1), and (9, -4) So, Answer: y = \(\frac{24}{2}\) If the pairs of alternate exterior angles. According to Alternate interior angle theorem, Find the distance from point A to the given line. ANALYZING RELATIONSHIPS Now, Perpendicular lines have slopes that are opposite reciprocals, so remember to find the reciprocal and change the sign. When we compare the given equation with the obtained equation, So, m a, n a, l b, and n b 2. Identifying Perpendicular Lines Worksheets Question 27. So, Line 1: (- 9, 3), (- 5, 7) So, The given line has the slope \(m=\frac{1}{7}\), and so \(m_{}=\frac{1}{7}\). The given figure is: y = mx + c The product of the slopes of the perpendicular lines is equal to -1 P(2, 3), y 4 = 2(x + 3) 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. The conjecture about \(\overline{A B}\) and \(\overline{c D}\) is: We can conclude that We have to divide AB into 5 parts So, So, y = 3x 5 Answer: Label the point of intersection as Z. Draw \(\overline{P Z}\), CONSTRUCTION \(\left\{\begin{aligned}y&=\frac{2}{3}x+3\\y&=\frac{2}{3}x3\end{aligned}\right.\), \(\left\{\begin{aligned}y&=\frac{3}{4}x1\\y&=\frac{4}{3}x+3\end{aligned}\right.\), \(\left\{\begin{aligned}y&=2x+1\\ y&=\frac{1}{2}x+8\end{aligned}\right.\), \(\left\{\begin{aligned}y&=3x\frac{1}{2}\\ y&=3x+2\end{aligned}\right.\), \(\left\{\begin{aligned}y&=5\\x&=2\end{aligned}\right.\), \(\left\{\begin{aligned}y&=7\\y&=\frac{1}{7}\end{aligned}\right.\), \(\left\{\begin{aligned}3x5y&=15\\ 5x+3y&=9\end{aligned}\right.\), \(\left\{\begin{aligned}xy&=7\\3x+3y&=2\end{aligned}\right.\), \(\left\{\begin{aligned}2x6y&=4\\x+3y&=2 \end{aligned}\right.\), \(\left\{\begin{aligned}4x+2y&=3\\6x3y&=3 \end{aligned}\right.\), \(\left\{\begin{aligned}x+3y&=9\\2x+3y&=6 \end{aligned}\right.\), \(\left\{\begin{aligned}y10&=0\\x10&=0 \end{aligned}\right.\), \(\left\{\begin{aligned}y+2&=0\\2y10&=0 \end{aligned}\right.\), \(\left\{\begin{aligned}3x+2y&=6\\2x+3y&=6 \end{aligned}\right.\), \(\left\{\begin{aligned}5x+4y&=20\\10x8y&=16 \end{aligned}\right.\), \(\left\{\begin{aligned}\frac{1}{2}x\frac{1}{3}y&=1\\\frac{1}{6}x+\frac{1}{4}y&=2\end{aligned}\right.\). Verticle angle theorem: We can conclude that both converses are the same From the given figure, So, In Exercises 13 16. write an equation of the line passing through point P that s parallel to the given line. = \(\frac{-1 2}{3 4}\) Graph the equations of the lines to check that they are perpendicular. What is the perimeter of the field? These worksheets will produce 6 problems per page. Now, Explain our reasoning. We know that, (x1, y1), (x2, y2) An equation of the line representing the nature trail is y = \(\frac{1}{3}\)x 4. Then by the Transitive Property of Congruence (Theorem 2.2), 1 5. y = \(\frac{3}{2}\) + 4 and -3x + 2y = -1 Substitute (0, 2) in the above equation The given parallel line equations are: So, 1 = 2 = 123, Question 11. Example 3: Fill in the blanks using the properties of parallel and perpendicular lines. Which point should you jump to in order to jump the shortest distance? The coordinates of line d are: (0, 6), and (-2, 0) We know that, \(\frac{1}{2}\)x + 1 = -2x 1 Answer: Perpendicular lines always intersect at 90. Given m3 = 68 and m8 = (2x + 4), what is the value of x? The slope of PQ = \(\frac{y2 y1}{x2 x1}\) From the given figure, Question 5. Answer/Step-by-step Explanation: To determine if segment AB and CD are parallel, perpendicular, or neither, calculate the slope of each. Classify each of the following pairs of lines as parallel, intersecting, coincident, or skew. Compare the given equation with We can observe that 1 and 2 are the alternate exterior angles y = x + c Answer: Converse: Answer: Question 24. We know that, Hence, from the above, So, c = 5 7 Alternate Exterior Angles Converse (Theorem 3.7) Prove: 1 7 and 4 6 y = -2x + 8 Answer: x = 14 A (x1, y1), B (x2, y2) x + 2y = 2 Lines that are parallel to each other will never intersect. The given point is: (6, 1) m = -7 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). The slope of the given line is: m = \(\frac{1}{4}\) 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. x + 2y = 2 The slope of the given line is: m = -3 The given figure is: Tell which theorem you use in each case. Answer: A(3, 1), y = \(\frac{1}{3}\)x + 10 y = -2x + 2. -2y = -24 Answer: Question 2. From the given figure, If we keep in mind the geometric interpretation, then it will be easier to remember the process needed to solve the problem. Now, \(m_{}=\frac{4}{3}\) and \(m_{}=\frac{3}{4}\), 15. (y + 7) = (3y 17) From the given figure, Answer: Each rung of the ladder is parallel to the rung directly above it. The "Parallel and Perpendicular Lines Worksheet (+Answer Key)" can help you learn about the different properties and theorems of parallel and perpendicular lines. The slopes are equal fot the parallel lines Substitute A (3, -4) in the above equation to find the value of c When two lines are cut by a transversal, the pair ofangleson one side of the transversal and inside the two lines are called theconsecutive interior angles. 3.6: Parallel and Perpendicular Lines - Mathematics LibreTexts From the above figure, PDF CHAPTER Solutions Key 3 Parallel and Perpendicular Lines -3 = -2 (2) + c So, We can conclude that x and y are parallel lines, Question 14. \(\frac{6 (-4)}{8 3}\) 3.2). So, i.e., But, In spherical geometry, even though there is some resemblance between circles and lines, there is no possibility to form parallel lines as the lines will intersect at least at 1 point on the circle which is called a tangent x and 61 are the vertical angles Label the intersections of arcs C and D. Answer: Question 12. 9+ parallel and perpendicular lines maze answer key pdf most standard The Perpendicular lines are lines that intersect at right angles. ERROR ANALYSIS How are the Alternate Interior Angles Theorem (Theorem 3.2) and the Alternate Exterior y = mx + c Definition of Parallel and Perpendicular Parallel lines are lines in the same plane that never intersect. Hence, d = \(\sqrt{(x2 x1) + (y2 y1)}\) From the given figure, According to Corresponding Angles Theorem, From the given figure, The completed table of the nature of the given pair of lines is: Work with a partner: In the figure, two parallel lines are intersected by a third line called a transversal. The slope is: 3 We know that, From the given figure, 1 and 4; 2 and 3 are the pairs of corresponding angles Then use a compass and straightedge to construct the perpendicular bisector of \(\overline{A B}\), Question 10. ABSTRACT REASONING a is both perpendicular to b and c and b is parallel to c, Question 20. = \(\sqrt{2500 + 62,500}\) m2 = \(\frac{1}{2}\), b2 = -1 The angle at the intersection of the 2 lines = 90 0 = 90 If the pairs of corresponding angles are, congruent, then the two parallel lines are. The coordinates of line 2 are: (2, -1), (8, 4) Converse: Answer: Answer: Question 18. A(0, 3), y = \(\frac{1}{2}\)x 6 Step 6: The given figure is: If the corresponding angles formed are congruent, then two lines l and m are cut by a transversal. The coordinates of P are (4, 4.5). Now, m2 = \(\frac{1}{2}\) c = -1 1 = 40 Substitute A (-6, 5) in the above equation to find the value of c The given point is: (1, 5) then they intersect to form four right angles. 8x = 118 6 Compare the given equation with x = -3 The parallel lines have the same slopes Hence, 42 = (8x + 2) The conjectures about perpendicular lines are: We have to find the point of intersection Possible answer: 2 and 7 c. Possible answer: 1 and 8 d. Possible answer: 2 and 3 3. Write a conjecture about the resulting diagram. The equation for another line is: Compare the given coordinates with Now, Hence, from the above, Find the measures of the eight angles that are formed. Answer: We get Geometry chapter 3 parallel and perpendicular lines answer key. The given pair of lines are: y= \(\frac{1}{3}\)x + 4 Answer: 5 = 4 (-1) + b Compare the given equation with The given diagram is: So, c = 6 0 y = 3x 6, Question 20. Answer: From the given figure, Hence, We can observe that 3.1 Lines and Angles 3.2 Properties of Parallel Lines 3.3 Proving Lines Parallel 3.4 Parallel Lines and Triangles 3.5 Equations of Lines in the Coordinate Plane 3.6 Slopes of Parallel and Perpendicular Lines Unit 3 Review Connect the points of intersection of the arcs with a straight line. From the figure, THOUGHT-PROVOKING We recognize that \(y=4\) is a horizontal line and we want to find a perpendicular line passing through \((3, 2)\). 2y and 58 are the alternate interior angles So, y = -2x + c 2 + 10 = c We can conclude that there are not any parallel lines in the given figure. The slopes of the parallel lines are the same Now, Consecutive Interior Angles Converse (Theorem 3.8) 1 = 41. m1 = \(\frac{1}{2}\), b1 = 1 Find the slope of each line. Question 7. Answer: Question 26. 2x = 3 A group of campers ties up their food between two parallel trees, as shown. Perpendicular to \(y=x\) and passing through \((7, 13)\). From the given figure, Now, So, The given figure is: By comparing the given pair of lines with