y = -2x -2 m2 = -1 y = 3x 5 So, Hence, Lines Perpendicular to a Transversal Theorem (Theorem 3.12): In a plane. A(0, 3), y = \(\frac{1}{2}\)x 6 So, y = -2x + \(\frac{9}{2}\) (2) y = \(\frac{1}{2}\)x 7 So, By using the parallel lines property, We know that, -1 = \(\frac{1}{2}\) ( 6) + c 4 5, b. The given point is: P (4, -6) 4 = 2 (3) + c Use the steps in the construction to explain how you know that\(\overline{C D}\) is the perpendicular bisector of \(\overline{A B}\). We can conclude that the distance that the two of the friends walk together is: 255 yards. b = 9 m is the slope Let the congruent angle be P Why does a horizontal line have a slope of 0, but a vertical line has an undefined slope? Hence, from the above, The slopes of the parallel lines are the same Parallel lines are two lines that are always the same exact distance apart and never touch each other. What can you conclude? Question 15. Answer: We can conclude that quadrilateral JKLM is a square. Answer: Question 2. The coordinates of line a are: (2, 2), and (-2, 3) 2x = 120 Answer: If two parallel lines are cut by a transversal, then the pairs of Alternate interior angles are congruent. Answer: 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. So, 3 + 133 = 180 (By using the Consecutive Interior angles theorem) Lines l and m are parallel. b. 1) = \(\sqrt{30.25 + 2.25}\) We can conclude that the line that is perpendicular to \(\overline{C D}\) is: \(\overline{A D}\) and \(\overline{C B}\), Question 6. We can conclude that the alternate interior angles are: 4 and 5; 3 and 6, Question 14. Copy and complete the following paragraph proof of the Alternate Interior Angles Converse using the diagram in Example 2. Where, Question 42. 17x = 180 27 d. AB||CD // Converse of the Corresponding Angles Theorem Answer: Answer: Now, Question 31. (\(\frac{1}{3}\)) (m2) = -1 Now, x = 12 A(- 2, 1), B(4, 5); 3 to 7 answer choices y = -x + 4 y = x + 6 y = 3x - 5 y = 2x Question 6 300 seconds Q. y = -x + c Substitute the given point in eq. From the figure, 6x = 140 53 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. We can conclude that -5 8 = c m2 = \(\frac{1}{2}\) y = mx + c If the pairs of alternate exterior angles. If we represent the bars in the coordinate plane, we can observe that the number of intersection points between any bar is: 0 Possible answer: 1 and 3 b. We can conclude that y = 3x 6, Question 20. \(m_{}=\frac{3}{4}\) and \(m_{}=\frac{4}{3}\), 3. If two lines x and y are horizontal lines and they are cut by a vertical transversal z, then Since you are given a point and the slope, use the point-slope form of a line to determine the equation. A(- 2, 4), B(6, 1); 3 to 2 We can conclude that 1 and 5 are the adjacent angles, Question 4. P = (4 + (4 / 5) 7, 1 + (4 / 5) 1) Notice that the slope is the same as the given line, but the \(y\)-intercept is different. m = \(\frac{0 2}{7 k}\) m1 m2 = -1 By the Vertical Angles Congruence Theorem (Theorem 2.6). Use a graphing calculator to verify your answer. We know that, m = \(\frac{1}{2}\) b = 19 Horizontal and vertical lines are perpendicular to each other. The given equation is: X (-3, 3), Y (3, 1) We can rewrite the equation of any horizontal line, \(y=k\), in slope-intercept form as follows: Written in this form, we see that the slope is \(m=0=\frac{0}{1}\). The slope of the perpendicular line that passes through (1, 5) is: We can observe that So, y = x + c c = 5 + 3 We can observe that We can conclude that AC || DF, Question 24. (8x + 6) = 118 (By using the Vertical Angles theorem) Explain your reasoning. The given rectangular prism of Exploration 2 is: The product of the slopes of perpendicular lines is equal to -1 If we draw the line perpendicular to the given horizontal line, the result is a vertical line. HOW DO YOU SEE IT? y = -2x + 1, e. b. Now, AP : PB = 3 : 7 The given figure is; So, We can conclude that the slope of the given line is: 3, Question 3. PROVING A THEOREM y = -2x 2, f. When the corresponding angles are congruent, the two parallel lines are cut by a transversal Yes, I support my friends claim, Explanation: So, So, Hence, from the above, Explain your reasoning. The equation that is perpendicular to the given line equation is: The product of the slopes of the perpendicular lines is equal to -1 Slope of ST = \(\frac{2}{-4}\) So, Explain. y = \(\frac{1}{3}\)x + 10 We know that, y = \(\frac{7}{2}\) 3 2x = -6 Write the equation of the line that is perpendicular to the graph of 9y = 4x , and whose y-intercept is (0, 3). then they are parallel. (6, 1); m = 3 It is given that From the above figure, 4.5 Equations of Parallel and Perpendicular Lines Solving word questions In this case, the negative reciprocal of 1/5 is -5. Proof: The equation for another perpendicular line is: XY = \(\sqrt{(3 + 3) + (3 1)}\) The product of the slopes of the perpendicular lines is equal to -1 Now, So, The two slopes are equal , the two lines are parallel. 3 + 4 + 5 = 180 A gazebo is being built near a nature trail. A(- 9, 3), y = x 6 (C) 2x = 180 Question 16. justify your answer. We know that, Hence, We know that, WRITING Justify your answer with a diagram. Hence, from the above, So, Substitute (2, -2) in the above equation Parallel to \(x=2\) and passing through (7, 3)\). Slope (m) = \(\frac{y2 y1}{x2 x1}\) We can solve it by using the "point-slope" equation of a line: y y1 = 2 (x x1) And then put in the point (5,4): y 4 = 2 (x 5) That is an answer! When two lines are crossed by another line (which is called the Transversal), theanglesin matching corners are calledcorresponding angles. So, They are not parallel because they are intersecting each other. The given points are: Is your classmate correct? The given figure is: From the given figure, Answer: Question 12. y = 180 48 We can observe that By using the linear pair theorem, So, y = mx + c When finding an equation of a line perpendicular to a horizontal or vertical line, it is best to consider the geometric interpretation. An engaging digital escape room for finding the equations of parallel and perpendicular lines. Since, It is given that m || n By comparing the slopes, The perpendicular line equation of y = 2x is: We can conclude that The given statement is: Hence, From the given figure, c = 5 \(\frac{1}{2}\) Intersecting lines share exactly one point that is where they meet each other, which is called the point of intersection. We can conclude that the converse we obtained from the given statement is true The line y = 4 is a horizontal line that have the straight angle i.e., 0 In Euclidean geometry, the two perpendicular lines form 4 right angles whereas, In spherical geometry, the two perpendicular lines form 8 right angles according to the Parallel lines Postulate in spherical geometry. BCG and __________ are corresponding angles. Corresponding Angles Theorem: We can observe that 48 and y are the consecutive interior angles and y and (5x 17) are the corresponding angles 2 and 3 are the consecutive interior angles Explain your reasoning. The given point is: (3, 4) We know that, y = \(\frac{3}{5}\)x \(\frac{6}{5}\) According to the Vertical Angles Theorem, the vertical angles are congruent y = mx + c These lines can be identified as parallel lines. Parallel Lines - Lines that move in their specific direction without ever intersecting or meeting each other at a point are known as the parallel lines. a = 1, and b = -1 The slope of line l is greater than 0 and less than 1. The two lines are Skew when they do not intersect each other and are not coplanar, Question 5. Answer: Hence, In this case, the slope is \(m_{}=\frac{1}{2}\) and the given point is \((8, 2)\). a. Answer: Answer: Let's expand 2 (x 5) and then rearrange: y 4 = 2x 10. b) Perpendicular to the given line: alternate interior, alternate exterior, or consecutive interior angles. Question 12. To find the value of c, The given coplanar lines are: Examine the given road map to identify parallel and perpendicular streets. PROOF From the given figure, 3 = 47 \(\overline{C D}\) and \(\overline{A E}\) Alternate Interior Angles are a pair of angleson the inner side of each of those two lines but on opposite sides of the transversal. Slope of AB = \(\frac{1}{7}\) We can conclude that the values of x and y are: 9 and 14 respectively. Write an equation for a line parallel to y = 1/3x - 3 through (4, 4) Q. = \(\sqrt{(4 5) + (2 0)}\) They are not perpendicular because they are not intersecting at 90. Select the orange Get Form button to start editing. Answer: m1 m2 = \(\frac{1}{2}\) 2 We know that, We can conclude that (50, 175), (500, 325) Question 23. y = \(\frac{1}{2}\)x 3 Line b and Line c are perpendicular lines. Hence, Write the equation of the line that is perpendicular to the graph of 53x y = , and The distance that the two of you walk together is: You and your mom visit the shopping mall while your dad and your sister visit the aquarium. The point of intersection = (0, -2) y = -2x + 2, Question 6. In Example 2, can you use the Perpendicular Postulate to show that is not perpendicular to ? So, Now, \(\overline{D H}\) and \(\overline{F G}\) are Skew lines because they are not intersecting and are non coplanar, Question 1. Answer: We know that, Question 21. Tell which theorem you use in each case. We can observe that there are 2 pairs of skew lines We know that, Compare the given equations with Let the given points are: 12. The slopes of the parallel lines are the same Answer: Hence, from the above, = 3, The slope of line d (m) = \(\frac{y2 y1}{x2 x1}\) Think of each segment in the figure as part of a line. We can conclude that = 6.26 y = 3x 5 Find the perpendicular line of y = 2x and find the intersection point of the two lines \(\frac{1}{3}\)x 2 = -3x 2 MAKING AN ARGUMENT Hence, from the above, Answer: b. m1 + m4 = 180 // Linear pair of angles are supplementary x = 4 In Exercises 3 6. find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. Examples of perpendicular lines: the letter L, the joining walls of a room. m = \(\frac{1}{6}\) and c = -8 We can conclude that the number of points of intersection of parallel lines is: 0, a. = 44,800 square feet So, So, We can observe that Hence, from the above, We get Answer: \(\frac{8 (-3)}{7 (-2)}\) y = -x 1, Question 18. Compare the given points with y = mx + c 8x = 42 2 a) Parallel to the given line: Hence, from the above, 2017 a level econs answer 25x30 calculator Angle of elevation calculator find distance Best scientific calculator ios P || L1 The length of the field = | 20 340 | (- 1, 5); m = 4 We can conclude that the number of points of intersection of coincident lines is: 0 or 1. The postulates and theorems in this book represent Euclidean geometry. Answer: Question 26. If it is warm outside, then we will go to the park Hence, from the above, lines intersect at 90. Explain why the top rung is parallel to the bottom rung. Which line(s) or plane(s) contain point B and appear to fit the description? The given equation is: Two lines that do not intersect and are also not parallel are ________ lines. From the given figure, When we compare the given equation with the obtained equation, Compare the given coordinates with Question 3. From the given figure, Given 1 3 These worksheets will produce 6 problems per page. We can conclude that the length of the field is: 320 feet, b. c = \(\frac{37}{5}\) (6, 22); y523 x1 4 13. The Converse of the Alternate Interior Angles Theorem states that if two lines are cut by a transversal and the alternate interior anglesare congruent, then the lines are parallel XY = \(\sqrt{(x2 x1) + (y2 y1)}\) If the slope of two given lines are negative reciprocals of each other, they are identified as perpendicular lines. COMPLETE THE SENTENCE Question 1. plane(s) parallel to plane CDH -3 = -2 (2) + c We know that, To find the value of b, From the given figure, We know that, 3 = 68 and 8 = (2x + 4) A (x1, y1), and B (x2, y2) For perpendicular lines, = \(\frac{0}{4}\) Answer: Question 40. Hence, from the above, We can observe that the product of the slopes are -1 and the y-intercepts are different Now, MATHEMATICAL CONNECTIONS Slope of QR = \(\frac{-2}{4}\) So, y = -3x + b (1) Hence, from the above, Answer: (x1, y1), (x2, y2) A(6, 1), y = 2x + 8 Now, Draw \(\overline{A B}\), as shown. d = \(\sqrt{(300 200) + (500 150)}\) Now, c = 12 Question 37. Find the equation of the line passing through \((8, 2)\) and perpendicular to \(6x+3y=1\). These Parallel and Perpendicular Lines Worksheets are great for practicing identifying perpendicular lines from pictures. Question 8. = | 4 + \(\frac{1}{2}\) | Consider the 2 lines L1 and L2 intersected by a transversal line L3 creating 2 corresponding angles 1 and 2 which are congruent No, there is no enough information to prove m || n, Question 18. x = 9. 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 ? Given 1 2, 3 4 Here 'a' represents the slope of the line. So, We can conclude that the consecutive interior angles of BCG are: FCA and BCA. Proof of Alternate exterior angles Theorem: The equation of the line along with y-intercept is: The equation that is parallel to the given equation is: Embedded mathematical practices, exercises provided make it easy for you to understand the concepts quite quickly. So, y = -x + 8 Hence, from the above, 42 and 6(2y 3) are the consecutive interior angles = \(\sqrt{(3 / 2) + (3 / 2)}\) Answer: By comparing the given equation with It is given that m || n The given equation is: d = \(\sqrt{(x2 x1) + (y2 y1)}\) Through the point \((6, 1)\) we found a parallel line, \(y=\frac{1}{2}x4\), shown dashed. PDF Name: Unit 3: Parallel & Perpendicular Lines Bell: Homework 5: Linear. Are the two linear equations parallel, perpendicular, or neither? -5 = \(\frac{1}{2}\) (4) + c Hence, from the above, We know that, Hence, from the given figure, Answer: The given point is: A (-1, 5) 3 = 76 and 4 = 104 The given point is: (1, 5) The given figure is: m1 m2 = -1 Hence, from the above, To be proficient in math, you need to communicate precisely with others. ABSTRACT REASONING Answer: y = x 6 We know that, We can conclude that the distance from point C to AB is: 12 cm. c = 2 0 (1) Sketch what the segments in the photo would look like if they were perpendicular to the crosswalk. In Exercises 21-24. are and parallel? m1 m2 = -1 y = \(\frac{3}{2}\)x + c From the figure, y = -x -(1) To find the coordinates of P, add slope to AP and PB Hence, The equation of the line that is perpendicular to the given line equation is: Answer: Question 50. y = -x + c So, We know that, We know that, Which type of line segment requires less paint? Proof: Question 17. 0 = \(\frac{1}{2}\) (4) + c We can conclude that the third line does not need to be a transversal. Find m1 and m2. We can observe that According to Perpendicular Transversal Theorem, = 2, The slope of line c (m) = \(\frac{y2 y1}{x2 x1}\) The given figure is: Answer: Answer: We can observe that the slopes are the same and the y-intercepts are different From the given figure, c = 5 Parallel and perpendicular lines have one common characteristic between them. Question 9. What is m1? Which theorem is the student trying to use? Then use the slope and a point on the line to find the equation using point-slope form. These Parallel and Perpendicular Lines Worksheets will ask the student to find the equation of a perpendicular line passing through a given equation and point. (x1, y1), (x2, y2) Now, According to the Perpendicular Transversal Theorem, The line parallel to \(\overline{Q R}\) is: \(\overline {L M}\), Question 3. So, Question 1. x + 2y = 2 The slope of the vertical line (m) = Undefined. b. \(\frac{1}{2}\)x + 7 = -2x + \(\frac{9}{2}\) So, Hence, 1 = 53.7 and 5 = 53.7 We can conclude that the Corresponding Angles Converse is the converse of the Corresponding Angles Theorem, Question 3. Hence, from the above, So, b. m1 + m4 = 180 // Linear pair of angles are supplementary The Parallel and Perpendicular Lines Worksheets are randomly created and will never repeat so you have an endless supply of quality Parallel and Perpendicular Lines Worksheets to use in the classroom or at home. 200), d. What is the distance from the meeting point to the subway? The given figure is: Answer: We know that, Now, By using the Consecutive Interior angles Converse, The standard linear equation is: We can conclude that the given pair of lines are non-perpendicular lines, work with a partner: Write the number of points of intersection of each pair of coplanar lines. Let us learn more about parallel and perpendicular lines in this article. Hence, from the above, The given points are: Question 29. Name two pairs of congruent angles when \(\overline{A D}\) and \(\overline{B C}\) are parallel? AP : PB = 4 : 1 x and 97 are the corresponding angles The point of intersection = (-1, \(\frac{13}{2}\)) Hence, Answer: 2x = 135 15 2. We know that, So, We know that, It is given that your school has a budget of $1,50,000 but we only need $1,20,512 A (x1, y1), B (x2, y2) The Skew lines are the lines that do not present in the same plane and do not intersect The Skew lines are the lines that are not parallel, non-intersect, and non-coplanar Answer: line(s) skew to . Prove 1 and 2 are complementary 2 and 3 We know that, Write an equation of the line that passes through the given point and is 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 The given equation is: (4.3.1) - Parallel and Perpendicular Lines Parallel lines have the same slope and different y- intercepts. A(8, 2),y = 4x 7 The given equation is: MODELING WITH MATHEMATICS AB = 4 units Answer: We can conclude that The "Parallel and Perpendicular Lines Worksheet (+Answer Key)" can help you learn about the different properties and theorems of parallel and perpendicular lines. Answer: Question 32. d = \(\sqrt{(x2 x1) + (y2 y1)}\) y = -2x + 3 We know that, The equation of the line along with y-intercept is: Now, REASONING You meet at the halfway point between your houses first and then walk to school. corresponding Answer: Given Slopes of Two Lines Determine if the Lines are Parallel, Perpendicular, or Neither Prove: c || d Hence, from the above, But it might look better in y = mx + b form. Perpendicular lines always intersect at right angles. Alternate Interior angles are a pair of angleson the inner side of each of those two lines but on opposite sides of the transversal. We know that, c = -5 Algebra 1 worksheet 36 parallel and perpendicular lines answer key. So, They are always equidistant from each other. We know that, So, We can conclude that We can observe that 8 = 180 115 Answer: Now, By comparing the given pair of lines with We know that, Here the given line has slope \(m=\frac{1}{2}\), and the slope of a line parallel is \(m_{}=\frac{1}{2}\). The lines that have an angle of 90 with each other are called Perpendicular lines Compare the given points with y = -3x + 650 y = -2x + 2. 8x = 118 6 Hence, from the above, FCJ and __________ are alternate interior angles. Given m1 = 105, find m4, m5, and m8. Perpendicular lines intersect at each other at right angles So, Lines AB and CD are not intersecting at any point and are always the same distance apart. 2 = 122 ERROR ANALYSIS Answer: m || n is true only when x and 73 are the consecutive interior angles according to the Converse of Consecutive Interior angles Theorem Find m1. From the given figure, The are outside lines m and n, on . Answer: d = \(\sqrt{(x2 x1) + (y2 y1)}\) = \(\sqrt{(3 / 2) + (3 / 4)}\) Give four examples that would allow you to conclude that j || k using the theorems from this lesson. According to the Perpendicular Transversal Theorem, This no prep unit bundle will assist your college students perceive parallel strains and transversals, parallel and perpendicular strains proofs, and equations of parallel and perpendicular. x || y is proved by the Lines parallel to Transversal Theorem. We can conclude that \(\overline{P R}\) and \(\overline{P O}\) are not perpendicular lines. y= \(\frac{1}{3}\)x + 4 The given point is: A (2, 0) Compare the given points with (x1, y1), (x2, y2) y = 2x + c2, b. All its angles are right angles. Find the value of x that makes p || q. Hence, Now, From the given figure, Parallel to \(10x\frac{5}{7}y=12\) and passing through \((1, \frac{1}{2})\). 0 = \(\frac{5}{3}\) ( -8) + c Slope of AB = \(\frac{2}{3}\) Similarly, observe the intersecting lines in the letters L and T that have perpendicular lines in them. d = | c1 c2 | The given equation is: Answer: You will find Solutions to all the BIM Book Geometry Ch 3 Parallel and Perpendicular Concepts aligned as per the BIM Textbooks. The points are: (-3, 7), (0, -2) Your classmate claims that no two nonvertical parallel lines can have the same y-intercept. MATHEMATICAL CONNECTIONS 3.12) According to the Converse of the Corresponding Angles Theorem, m || n is true only when the corresponding angles are congruent Answer: 68 + (2x + 4) = 180 Answer: Prove 2 4 y = 2x + 7. m = \(\frac{3}{-1.5}\) Now, Question 5. intersecting Answer: Explanation: Substitute P (4, 0) in the above equation to find the value of c y = -7x 2. Substitute (1, -2) in the above equation Find the slope of a line perpendicular to each given line. ATTENDING TO PRECISION Often you will be asked to find the equation of a line given some geometric relationshipfor instance, whether the line is parallel or perpendicular to another line. b. Find m2. The slope of the given line is: m = \(\frac{1}{4}\) We know that, When we compare the given equation with the obtained equation, Hence, from the above, This contradicts what was given,that angles 1 and 2 are congruent. So, Compare the given equation with A triangle has vertices L(0, 6), M(5, 8). 1 = 180 57 You and your friend walk to school together every day. In Exercises 3 6, think of each segment in the diagram as part of a line. MODELING WITH MATHEMATICS The intersection point of y = 2x is: (2, 4) y = \(\frac{1}{2}\)x 4, Question 22. y = 2x + 3, Question 23. It is given that l || m and l || n, The given equation is: The given statement is: Answer: Question 16. We can observe that the slopes are the same and the y-intercepts are different We know that, Answer: Substitute (0, 2) in the above equation We can conclude that the vertical angles are: It is given that the two friends walk together from the midpoint of the houses to the school The diagram that represents the figure that it can not be proven that any lines are parallel is: So, 1 = 32 So, Explain your reasoning. We know that, We can conclude that 42 and 48 are the vertical angles, Question 4. b) Perpendicular to the given line: Compare the given points with Now, So, You decide to meet at the intersection of lines q and p. Each unit in the coordinate plane corresponds to 50 yards. According to the Consecutive Exterior angles Theorem, If two sides of two adjacent acute angles are perpendicular, then the angles are complementary. 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. Question 45. The given figure is: So, y = \(\frac{1}{5}\)x + c For example, the letter H, in which the vertical lines are parallel and the horizontal line is perpendicular to both the vertical lines. The coordinates of the line of the second equation are: (-4, 0), and (0, 2) The corresponding angles are: and 5; 4 and 8, b. alternate interior angles Enter a statement or reason in each blank to complete the two-column proof. Write the Given and Prove statements. WHICH ONE did DOESNT BELONG? From the given figure, Hence, Determine the slope of a line perpendicular to \(3x7y=21\). y = \(\frac{1}{6}\)x 8 The lines skew to \(\overline{E F}\) are: \(\overline{C D}\), \(\overline{C G}\), and \(\overline{A E}\), Question 4. x 2y = 2 If the pairs of corresponding angles are, congruent, then the two parallel lines are. The product of the slopes of the perpendicular lines is equal to -1 When we compare the converses we obtained from the given statement and the actual converse, Answer: m = \(\frac{1}{4}\) Now, The third intersecting line can intersect at the same point that the two lines have intersected as shown below: Hence, from the above, Hence, from the above, y = \(\frac{1}{2}\)x + c y = mx + c Your school lies directly between your house and the movie theater. Perpendicular to \(y=2\) and passing through \((1, 5)\). So, The 2 pair of skew lines are: q and p; l and m, d. Prove that 1 2. P = (3.9, 7.6) Answer: Question 38. The given figure is: P = (3 + (3 / 5) 8, 2 + (3 / 5) 5) If m1 = 58, then what is m2? Hene, from the given options, We know that, Now, c = -13 The slope of perpendicular lines is: -1 So, (-3, 8); m = 2 The equation of the perpendicular line that passes through the midpoint of PQ is: 1. We know that, The given figure is: The letter A has a set of perpendicular lines. We can conclude that the corresponding angles are: 1 and 5; 3 and 7; 2 and 4; 6 and 8, Question 8. We can conclude that Hence, from the above, x = c Solution: We need to know the properties of parallel and perpendicular lines to identify them. . Answer: Answer: In Exercises 13 and 14, prove the theorem. Compare the given points with (x1, y1), and (x2, y2) The given figure is: Question 39. If the angle measure of the angles is a supplementary angle, then the lines cut by a transversal are parallel Now, 3.6 Slopes of Parallel and Perpendicular Lines Notes Key. Answer: We know that, (- 8, 5); m = \(\frac{1}{4}\) Line 2: (- 11, 6), (- 7, 2) We can observe that the given lines are perpendicular lines So, Hence. -1 = \(\frac{-2}{7 k}\) The given figure is: Key Question: If x = 115, is it possible for y to equal 115? (x1, y1), (x2, y2) We can observe that \(\overline{A C}\) is not perpendicular to \(\overline{B F}\) because according to the perpendicular Postulate, \(\overline{A C}\) will be a straight line but it is not a straight line when we observe Example 2 We can conclude that the value of x is: 107, Question 10. When you look at perpendicular lines they have a slope that are negative reciprocals of each other. S. Giveh the following information, determine which lines it any, are parallel. So, We can solve for \(m_{1}\) and obtain \(m_{1}=\frac{1}{m_{2}}\). y = \(\frac{1}{2}\)x + c To find the distance between E and \(\overline{F H}\), we need to find the distance between E and G i.e., EG So, We know that, The product of the slopes of the perpendicular lines is equal to -1 The equation that is perpendicular to the given line equation is: x = \(\frac{-6}{2}\) Is it possible for consecutive interior angles to be congruent? Question 1. y = \(\frac{1}{2}\)x + 2 Hence, from the above, line(s) skew to Explain. Answer: Question 26. 19) 5x + y = -4 20) x = -1 21) 7x - 4y = 12 22) x + 2y = 2 2x x = 56 2 (1) = Eq. So, 3y = x 50 + 525 11y = 96 19 We can conclude that option D) is correct because parallel and perpendicular lines have to be lie in the same plane, Question 8. Since two parallel lines never intersect each other and they have the same steepness, their slopes are always equal. When we compare the given equation with the obtained equation, c = \(\frac{16}{3}\) Often you have to perform additional steps to determine the slope.

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