A (x1, y1), and B (x2, y2) So, Alternate Exterior Angles Theorem: y = \(\frac{1}{2}\)x + 7 -(1) Vertical Angles Theoremstates thatvertical angles,anglesthat are opposite each other and formed by two intersecting straight lines, are congruent Answer: By comparing the given pair of lines with 1 (m2) = -3 Alternate exterior angles are the pair of anglesthat lie on the outer side of the two parallel lines but on either side of the transversal line y = 12 m a, n a, l b, and n b An equation of the line representing Washington Boulevard is y = \(\frac{2}{3}\)x. Line 1: (1, 0), (7, 4) 2x = -6 Then, let's go back and fill in the theorems. So, 12. \(\begin{aligned} 2x+14y&=7 \\ 2x+14y\color{Cerulean}{-2x}&=7\color{Cerulean}{-2x} \\ 14y&=-2x+7 \\ \frac{14y}{\color{Cerulean}{14}}&=\frac{-2x+7}{\color{Cerulean}{14}} \\ y&=\frac{-2x}{14}+\frac{7}{14} \\ y&=-\frac{1}{7}x+\frac{1}{2} \end{aligned}\). A(- 2, 3), y = \(\frac{1}{2}\)x + 1 So, Answer: 48 + y = 180 Using X and Y as centers and an appropriate radius, draw arcs that intersect. Substitute A (6, -1) in the above equation Answer: Given Slope of a Line Find Slopes for Parallel and Perpendicular Lines Worksheets 2 and7 Answer: So, Although parallel and perpendicular lines are the two basic and most commonly used lines in geometry, they are quite different from each other. y = mx + c Hence, from the above, So, We can conclude that there are not any parallel lines in the given figure, Question 15. So, So, The equation that is parallel to the given equation is: Hence, from the above, According to Alternate interior angle theorem, Work with a partner: Fold a piece of pair in half twice. y = mx + c We have to find the point of intersection Substitute A (-6, 5) in the above equation to find the value of c m is the slope Find the measures of the eight angles that are formed. (6, 1); m = 3 Perpendicular to \(6x+3y=1\) and passing through \((8, 2)\). y = mx + c c = 5 + 3 We know that, Answer: 2 = 123 Parallel and perpendicular lines can be identified on the basis of the following properties: If the slope of two given lines is equal, they are considered to be parallel lines. 2x + \(\frac{1}{2}\)x = 5 (1) = Eq. c = -12 1. Question 43. 2x + y = 180 18 Geometrically, we note that if a line has a positive slope, then any perpendicular line will have a negative slope. The slopes are equal fot the parallel lines \(\left\{\begin{aligned}y&=\frac{2}{3}x+3\\y&=\frac{2}{3}x3\end{aligned}\right.\), \(\left\{\begin{aligned}y&=\frac{3}{4}x1\\y&=\frac{4}{3}x+3\end{aligned}\right.\), \(\left\{\begin{aligned}y&=2x+1\\ y&=\frac{1}{2}x+8\end{aligned}\right.\), \(\left\{\begin{aligned}y&=3x\frac{1}{2}\\ y&=3x+2\end{aligned}\right.\), \(\left\{\begin{aligned}y&=5\\x&=2\end{aligned}\right.\), \(\left\{\begin{aligned}y&=7\\y&=\frac{1}{7}\end{aligned}\right.\), \(\left\{\begin{aligned}3x5y&=15\\ 5x+3y&=9\end{aligned}\right.\), \(\left\{\begin{aligned}xy&=7\\3x+3y&=2\end{aligned}\right.\), \(\left\{\begin{aligned}2x6y&=4\\x+3y&=2 \end{aligned}\right.\), \(\left\{\begin{aligned}4x+2y&=3\\6x3y&=3 \end{aligned}\right.\), \(\left\{\begin{aligned}x+3y&=9\\2x+3y&=6 \end{aligned}\right.\), \(\left\{\begin{aligned}y10&=0\\x10&=0 \end{aligned}\right.\), \(\left\{\begin{aligned}y+2&=0\\2y10&=0 \end{aligned}\right.\), \(\left\{\begin{aligned}3x+2y&=6\\2x+3y&=6 \end{aligned}\right.\), \(\left\{\begin{aligned}5x+4y&=20\\10x8y&=16 \end{aligned}\right.\), \(\left\{\begin{aligned}\frac{1}{2}x\frac{1}{3}y&=1\\\frac{1}{6}x+\frac{1}{4}y&=2\end{aligned}\right.\). Alternate Interior Anglesare a pair ofangleson the inner side of each of those two lines but on opposite sides of the transversal. Hence, from the above, (-1) (m2) = -1 your friend claims to be able to make the shot Shown in the diagram by hitting the cue ball so that m1 = 25. Now, Where, Compare the given points with Hence, from the above, c1 = 4 c. If m1 is 60, will ABC still he a straight angle? Is b c? When the corresponding angles are congruent, the two parallel lines are cut by a transversal d = | 6 4 + 4 |/ \(\sqrt{2}\)} y = -3 (0) 2 Consecutive Interior Angles Theorem (Thm. y = -3 It is given that your classmate claims that no two nonvertical parallel lines can have the same y-intercept What is the length of the field? Answer: 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 Converse of the Corresponding Angles Theorem: Proof: Answer: Question 36. Perpendicular to \(x=\frac{1}{5}\) and passing through \((5, 3)\). Answer: y = x \(\frac{28}{5}\) The given table is: When you look at perpendicular lines they have a slope that are negative reciprocals of each other. Answer: = 3, The slope of line d (m) = \(\frac{y2 y1}{x2 x1}\) The given figure is: Name two pairs of supplementary angles when \(\overline{A B}\) and \(\overline{D C}\) are parallel. It is given that From the given figure, m || n is true only when x and 73 are the consecutive interior angles according to the Converse of Consecutive Interior angles Theorem The given point is: (-8, -5) 1 and 3; 2 and 4; 5 and 7; 6 and 8, b. The coordinates of line b are: (3, -2), and (-3, 0) Question 25. Is it possible for all eight angles formed to have the same measure? The parallel line equation that is parallel to the given equation is: Hence, Question 15. Compare the given points with (x1, y1), and (x2, y2) Hence, from the above, Answer: k = 5 \(\overline{C D}\) and \(\overline{A E}\) Select all that apply. = \(\sqrt{30.25 + 2.25}\) We can conclude that the quadrilateral QRST is a parallelogram. 1 = 2 = 42, Question 10. y = 13 a. corresponding angles The line parallel to \(\overline{E F}\) is: \(\overline{D H}\), Question 2. a. The coordinates of line q are: We know that, The representation of the complete figure is: PROVING A THEOREM Answer: Corresponding Angles Theorem c = 2 1 Answer: The product of the slopes of the perpendicular lines is equal to -1 From the given figure, By using the Corresponding angles Theorem, Answer: We can conclude that b || a, Question 4. We can observe that the given pairs of angles are consecutive interior angles 4.7 of 5 (20 votes) Fill PDF Online Download PDF. HOW DO YOU SEE IT? We can conclude that the distance from line l to point X is: 6.32. We know that, m = -7 To find the value of c, substitute (1, 5) in the above equation c = -3 We can conclude that the distance from point E to \(\overline{F H}\) is: 7.07. Hence, from the above, So, We can conclude that a || b. We can conclude that the distance between the meeting point and the subway is: 364.5 yards, Question 13. Answer: 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). Embedded mathematical practices, exercises provided make it easy for you to understand the concepts quite quickly. Hence, from the above, To find the distance from line l to point X, Hence, from the above, Substitute the given point in eq. y y1 = m (x x1) The Alternate Interior Angles Theorem states that, when two parallel lines are cut by a transversal, the resultingalternate interior anglesare congruent We know that, These worksheets will produce 6 problems per page. A(3, 6) Slope of line 2 = \(\frac{4 6}{11 2}\) 3 + 4 + 5 = 180 If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles formed are supplementary y = mx + b Hence, from the above, So, Identify two pairs of parallel lines so that each pair is in a different plane. Hence, Let the given points are: How are the Alternate Interior Angles Theorem (Theorem 3.2) and the Alternate Exterior Decide whether it is true or false. Question 22. Where, According to the consecutive exterior angles theorem, x = \(\frac{112}{8}\) We can observe that From the argument in Exercise 24 on page 153, The given figure is: Question 23. Hence, The equation that is parallel to the given equation is: P(2, 3), y 4 = 2(x + 3) It is given that Hene, from the given options, Lines that are parallel to each other will never intersect. Parallel to \(y=\frac{3}{4}x3\) and passing through \((8, 2)\). The Coincident lines may be intersecting or parallel Hence, From the given figure, The slope of horizontal line (m) = 0 A (x1, y1), and B (x2, y2) The given point is: (6, 1) We know that, ANALYZING RELATIONSHIPS 3 + 133 = 180 (By using the Consecutive Interior angles theorem) Hence, b. = \(\sqrt{(-2 7) + (0 + 3)}\) 12y 18 = 138 \(\begin{aligned} y-y_{1}&=m(x-x_{1}) \\ y-(-2)&=\frac{1}{2}(x-8) \end{aligned}\). The equation of the perpendicular line that passes through the midpoint of PQ is: y = mx + c Substitute A (2, -1) in the above equation to find the value of c We can conclude that the distance from the given point to the given line is: 32, Question 7. Click the image to be taken to that Parallel and Perpendicular Lines Worksheet. y = -3x + 19, Question 5. CONSTRUCTING VIABLE ARGUMENTS XY = \(\sqrt{(x2 x1) + (y2 y1)}\) : n; same-side int. 61 and y are the alternate interior angles \(m_{}=\frac{4}{3}\) and \(m_{}=\frac{3}{4}\), 15. Hence, from the above, Question 22. Now, Answer: Answer: Answer: Question 36. We know that, Hence, Answer: Question 14. The lines that have the same slope and different y-intercepts are Parallel lines The given figure is: as corresponding angles formed by a transversal of parallel lines, and so, ANALYZING RELATIONSHIPS The line that is perpendicular to y=n is: So, = \(\sqrt{(6) + (6)}\) b.) So, So, We can conclude that THINK AND DISCUSS 1. ax + by + c = 0 y = \(\frac{1}{4}\)x + c So, (2) y = \(\frac{1}{2}\)x + 7 y = x + 9 The given figure is: Hence, Substitute A (2, 0) in the above equation to find the value of c Now, Slope of ST = \(\frac{2}{-4}\) Answer: Question 12. Slope (m) = \(\frac{y2 y1}{x2 x1}\) If the angle measure of the angles is a supplementary angle, then the lines cut by a transversal are parallel We can observe that we divided the total distance into the four congruent segments or pieces The given figure is: The Skew lines are the lines that are non-intersecting, non-parallel and non-coplanar y = \(\frac{1}{3}\)x + \(\frac{475}{3}\) = -3 Hence, from the above, A(-1, 5), y = \(\frac{1}{7}\)x + 4 Answer: 2x y = 4 From the coordinate plane, From the given figure, Answer: So, Question 25. The given point is: A (3, -1) Hence, from the above, Perpendicular transversal theorem: Furthermore, the rise and run between two perpendicular lines are interchanged. Now, b.) The equation of the line that is parallel to the line that represents the train tracks is: Some examples follow. Legal. Here is a graphic preview for all of the Parallel and Perpendicular Lines Worksheets. line(s) parallel to . Now, Where, Given 1 2, 3 4 Question 7. We have to find the point of intersection 2 and 11 Label the intersections of arcs C and D. The distance from the perpendicular to the line is given as the distance between the point and the non-perpendicular line HOW DO YOU SEE IT? The equation of the line that is parallel to the given line equation is: Question 20. It is given that the given angles are the alternate exterior angles Answer: The slopes are equal fot the parallel lines So, Hence, from the above, Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. The product of the slopes is -1 and the y-intercepts are different The given line has slope \(m=\frac{1}{4}\), and thus \(m_{}=+\frac{4}{1}=4\). Proof: The slope of the given line is: m = 4 We know that, y = -3x + 150 + 500 Simply click on the below available and learn the respective topics in no time. Write the equation of the line that is perpendicular to the graph of 53x y = , and Now, The equation that is parallel to the given equation is: Examine the given road map to identify parallel and perpendicular streets. and N(4, 1), Is the triangle a right triangle? y = -2x 1 (2) If two parallel lines are cut by a transversal, then the pairs of Corresponding angles are congruent. Any fraction that contains 0 in the numerator has its value equal to 0 MATHEMATICAL CONNECTIONS So, We can conclude that the line that is perpendicular to \(\overline{C D}\) is: \(\overline{A D}\) and \(\overline{C B}\), Question 6. The given diagram is: From the given figure, y = \(\frac{77}{11}\) d = | c1 c2 | The equation of the line along with y-intercept is: Hence, from the above, \(\overline{A B}\) and \(\overline{G H}\), b. a pair of perpendicular lines = (\(\frac{-2}{2}\), \(\frac{-2}{2}\)) = 0 What is the perimeter of the field? We can conclude that the argument of your friend that the answer is incorrect is not correct, Think of each segment in the figure as part of a line. Verify your answer. Answer: The vertical angles are congruent i.e., the angle measures of the vertical angles are equal AB = AO + OB XY = 6.32 Answer: Question 34. y = \(\frac{1}{2}\)x + c The given figure is: Since, The product of the slopes of the perpendicular lines is equal to -1 then they are congruent. y = 2x + c Find the equation of the line passing through \((\frac{7}{2}, 1)\) and parallel to \(2x+14y=7\). Give four examples that would allow you to conclude that j || k using the theorems from this lesson. Substitute (1, -2) in the above equation We can observe that the given angles are the corresponding angles Perpendicular to \(xy=11\) and passing through \((6, 8)\). Let us learn more about parallel and perpendicular lines in this article. Answer: Which theorems allow you to conclude that m || n? We want to prove L1 and L2 are parallel and we will prove this by using Proof of Contradiction Now, We can conclude that c = -13 We know that, Substitute (6, 4) in the above equation y = 27.4 This contradicts what was given,that angles 1 and 2 are congruent. So, The two pairs of perpendicular lines are l and n, c. Identify two pairs of skew line Whereas, if the slopes of two given lines are negative reciprocals of each other, they are considered to be perpendicular lines. y = 2x c = 7 9 \(m_{}=\frac{3}{2}\) and \(m_{}=\frac{2}{3}\), 19. Check out the following pages related to parallel and perpendicular lines. The equation of the line along with y-intercept is: For parallel lines, we cant say anything Question 8. y = \(\frac{1}{2}\)x 2 In Exploration 1, explain how you would prove any of the theorems that you found to be true. Which line(s) or plane(s) contain point B and appear to fit the description? line(s) parallel to . y = 7 We can observe that the given angles are corresponding angles Answer: Answer: Question 28. We know that, Hence, from the above, The product of the slopes of the perpendicular lines is equal to -1 We know that, Answer: The given point is: A (8, 2) Two nonvertical lines in the same plane, with slopes m1 and m2, are parallel if their slopes are the same, m1 = m2. Classify each pair of angles whose measurements are given. MAKING AN ARGUMENT In exercises 25-28. copy and complete the statement. The equation that is perpendicular to the given line equation is: b is the y-intercept Label points on the two creases. Identifying Perpendicular Lines Worksheets Substitute the given point in eq. 2x + y = 162(1) Question 37. We can conclude that the converse we obtained from the given statement is true Question 25. y = 4x + b (1) 2x x = 56 2 Hence, from the above, Answer: (-3, 8); m = 2 Write a conjecture about \(\overline{A O}\) and \(\overline{O B}\) Justify your conjecture. MATHEMATICAL CONNECTIONS y = mx + b Find the equation of the line passing through \((6, 1)\) and parallel to \(y=\frac{1}{2}x+2\). Exercise \(\PageIndex{3}\) Parallel and Perpendicular Lines. Hence, from the above, Hence, The given point is: (2, -4) y = \(\frac{1}{5}\)x + \(\frac{37}{5}\) Answer: y = 4 x + 2 2. y = 5 - 2x 3. The y-intercept is: 9. So, These worksheets will produce 10 problems per page. Answer: Sketch what the segments in the photo would look like if they were perpendicular to the crosswalk. Answer: Yes, your classmate is correct, Explanation: DRAWING CONCLUSIONS To be proficient in math, you need to analyze relationships mathematically to draw conclusions. We know that, We can observe that the given angles are the consecutive exterior angles Graph the equations of the lines to check that they are parallel. Now, The slopes of the parallel lines are the same Explain your reasoning. Write an equation of the line that passes through the given point and is parallel to the Get the best Homework key Hence, from the above, We can conclude that the value of XZ is: 7.07, Find the length of \(\overline{X Y}\) ax + by + c = 0 You and your friend walk to school together every day. DIFFERENT WORDS, SAME QUESTION When two lines are crossed by another line (which is called the Transversal), theanglesin matching corners are calledcorresponding angles. To find 4: Slope of MJ = \(\frac{0 0}{n 0}\) _____ lines are always equidistant from each other. y = \(\frac{1}{3}\)x + \(\frac{26}{3}\) (2) Answer: The equation of the line that is perpendicular to the given line equation is: Indulging in rote learning, you are likely to forget concepts. Now, Question 11. From the given figure, Answer: We have to divide AB into 8 parts The parallel lines have the same slopes Answer: Question 29. So, We can conclude that the lines that intersect \(\overline{N Q}\) are: \(\overline{N K}\), \(\overline{N M}\), and \(\overline{Q P}\), c. Which lines are skew to ? Answer: Answer: y = -2x + c m2 = -1 So, Label the ends of the crease as A and B. The map shows part of Denser, Colorado, Use the markings on the map. So, Eq. The given figure is; y = -2 P || L1 Answer: Answer: Question 12. So, i.e., THOUGHT-PROVOKING Hence, = 3 THOUGHT-PROVOKING We know that, m1m2 = -1 ERROR ANALYSIS So, We can conclude that the alternate interior angles are: 4 and 5; 3 and 6, Question 14. Draw \(\overline{A P}\) and construct an angle 1 on n at P so that PAB and 1 are corresponding angles Use an example to support your conjecture. So, What does it mean when two lines are parallel, intersecting, coincident, or skew? Answer: Slope of the line (m) = \(\frac{y2 y1}{x2 x1}\) So, Substitute A (3, -4) in the above equation to find the value of c (1) = Eq. It is given that m || n MODELING WITH MATHEMATICS So, 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. Now, (- 8, 5); m = \(\frac{1}{4}\) The equation of a line is: Slope of the line (m) = \(\frac{y2 y1}{x2 x1}\) Hence, from the above, We know that, Where, From the given figure, Question 4. We have to find the distance between A and Y i.e., AY Answer: Question 16. The resultant diagram is: (x1, y1), (x2, y2) Compare the given coordinates with (x1, y1), and (x2, y2) Find m1 and m2. Hence, from the above, Step 3: We know that, y = -2x Answer: The lines that have the slopes product -1 and different y-intercepts are Perpendicular lines Find the distance between the lines with the equations y = \(\frac{3}{2}\) + 4 and 3x + 2y = 1. The equation that is perpendicular to the given line equation is: Question 13. Since it must pass through \((3, 2)\), we conclude that \(x=3\) is the equation. We can conclude that the distance between the given 2 points is: 6.40. 9. So, Answer: XZ = 7.07 There are some letters in the English alphabet that have both parallel and perpendicular lines. To find the value of c, Substitute A (3, -1) in the above equation to find the value of c From the given figure, (7x + 24) = 108 8 = 65. Hence, from the above, Let's try the best Geometry chapter 3 parallel and perpendicular lines answer key. We can conclude that \(\overline{K L}\), \(\overline{L M}\), and \(\overline{L S}\), d. Should you have named all the lines on the cube in parts (a)-(c) except \(\overline{N Q}\)? We can conclude that the lines x = 4 and y = 2 are perpendicular lines, Question 6. It is given that Substitute P(-8, 0) in the above equation It is given that in spherical geometry, all points are points on the surface of a sphere. d = \(\sqrt{(x2 x1) + (y2 y1)}\) We know that, b is the y-intercept XZ = \(\sqrt{(x2 x1) + (y2 y1)}\) We can observe that the given angles are consecutive exterior angles If you use the diagram below to prove the Alternate Exterior Angles Converse. AP : PB = 3 : 2 (x1, y1), (x2, y2) y = \(\frac{10 12}{3}\) Name two pairs of congruent angles when \(\overline{A D}\) and \(\overline{B C}\) are parallel? Note: Parallel lines are distinguished by a matching set of arrows on the lines that are parallel. (13, 1) and (9, 4) If two lines are horizontal, then they are parallel We can conclude that The converse of the Alternate Interior angles Theorem: So, Answer: Question 38. Now, Question 13. 8x 4x = 24 = (\(\frac{8}{2}\), \(\frac{-6}{2}\)) Hence, from the given figure, c = 2 = \(\sqrt{(3 / 2) + (3 / 4)}\) Will the opening of the box be more steep or less steep? A(- 3, 7), y = \(\frac{1}{3}\)x 2 We have identifying parallel lines, identifying perpendicular lines, identifying intersecting lines, identifying parallel, perpendicular, and intersecting lines, identifying parallel, perpendicular, and intersecting lines from a graph, Given the slope of two lines identify if the lines are parallel, perpendicular or neither, Find the slope for any line parallel and the slope of any line perpendicular to the given line, Find the equation of a line passing through a given point and parallel to the given equation, Find the equation of a line passing through a given point and perpendicular to the given equation, and determine if the given equations for a pair of lines are parallel, perpendicular or intersecting for your use. a. All the angle measures are equal Answer: Question 35. The slopes of perpendicular lines are undefined and 0 respectively 9 = \(\frac{2}{3}\) (0) + b (5y 21) and 116 are the corresponding angles The product of the slopes of the perpendicular lines is equal to -1 Substitute (4, -5) in the above equation Question 3. -4 = \(\frac{1}{2}\) (2) + b = 2 (2) In this form, we see that perpendicular lines have slopes that are negative reciprocals, or opposite reciprocals. Substitute A (3, 4) in the above equation to find the value of c ABSTRACT REASONING The lines are named as AB and CD. y = \(\frac{2}{3}\)x + 1, c. The given equation is: construction change if you were to construct a rectangle? Name a pair of perpendicular lines. The parallel line needs to have the same slope of 2. Explain. A(3, 4),y = x + 8 We can conclude that the number of points of intersection of intersecting lines is: 1, c. The points of intersection of coincident lines: So, Question 3. So, 2 = \(\frac{1}{2}\) (-5) + c So, The lines that do not intersect to each other and are coplanar are called Parallel lines Question 1. Now, Answer: Question 34. The given point is: (1, 5) Geometrically, we see that the line \(y=4x1\), shown dashed below, passes through \((1, 5)\) and is perpendicular to the given line. Answer: The given figure is: ATTENDING TO PRECISION So, In Exercises 47 and 48, use the slopes of lines to write a paragraph proof of the theorem. 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? So, Therefore, these lines can be identified as perpendicular lines. = \(\frac{-3}{-4}\) We can conclude that Now, Examples of perpendicular lines: the letter L, the joining walls of a room. We can observe that Slope (m) = \(\frac{y2 y1}{x2 x1}\) Substitute (0, 2) in the above equation Therefore, the final answer is " neither "! m2 = \(\frac{2}{3}\) The representation of the given pair of lines in the coordinate plane is: c = \(\frac{16}{3}\) From the given figure, If so, dont bother as you will get a complete idea through our BIM Geometry Chapter 3 Parallel and Perpendicular Lines Answer Key. Connect the points of intersection of the arcs with a straight line. Answer: Given: k || l, t k Two lines are cut by a transversal. Hence, The slope of line a (m) = \(\frac{y2 y1}{x2 x1}\) We can conclude that 2 and 7 are the Vertical angles, Question 5. The given equations are: y = \(\frac{1}{2}\)x 4, Question 22. Compare the given equation with = \(\sqrt{31.36 + 7.84}\) c = 2 0 y = 2x + 12 x = 9 we know that, 1 = 53.7 and 5 = 53.7 y = 162 2 (9) When we compare the given equation with the obtained equation, y = \(\frac{1}{2}\)x + c The coordinates of line a are: (0, 2), and (-2, -2) Hence, from the above, x = c (8x + 6) = 118 (By using the Vertical Angles theorem) How would your i.e., To find the coordinates of P, add slope to AP and PB From the given figure, The slope of first line (m1) = \(\frac{1}{2}\) c. Use the properties of angles formed by parallel lines cut by a transversal to prove the theorem. The line parallel to \(\overline{Q R}\) is: \(\overline {L M}\), Question 3. The slope of one line is the negative reciprocal of the other line. The equation of the line along with y-intercept is: What is m1? A student says. The claim of your friend is not correct 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. Question 1. Line 2: (2, 1), (8, 4) Corresponding Angles Theorem (Theorem 3.1): If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. ABSTRACT REASONING So, an equation of the line that passes through the midpoint and is perpendicular to \(\overline{P Q}\). Answer: Question 40. From ESR, First, find the slope of the given line. The slope of the given line is: m = \(\frac{2}{3}\) By using the Alternate exterior angles Theorem, a. a) Parallel line equation: The equation that is parallel to the given equation is: The equation of the line along with y-intercept is: Now, x + 2y = 2 Answer: Question 30. We have to find 4, 5, and 8 The given point is: A (-1, 5) Slope of RS = \(\frac{-3}{-1}\) Answer: y = -7x 2. y = x + 4 (2) Answer: Question 18. According to the Consecutive Interior Angles Theorem, the sum of the consecutive interior angles is 180 Which rays are not parallel?