It is important to have a geometric understanding of this question. \(\overline{I J}\) and \(\overline{C D}\), c. a pair of paralIeI lines Answer: The given points are A (-1, 2), and B (3, -1) Compare the given points with A (x1, y1), B (x2, y2) m = Substitute A (-1, 2), and B (3, -1) in the formula. Is quadrilateral QRST a parallelogram? Which angle pair does not belong with the other three? c = 3 The given diagram is: (5y 21) = 116 (- 3, 7) and (8, 6) The given equation is: d = | x y + 4 | / \(\sqrt{1 + (-1)}\) These Parallel and Perpendicular Lines Worksheets are great for practicing identifying parallel lines from pictures. The equation of a line is: 1 + 2 = 180 Hence, When two lines are cut by a transversal, the pair ofangles on one side of the transversal and inside the two lines are called the Consecutive interior angles From the given diagram, Answer: Hence, from the above, y = -2x + 2 Explain. Answer: XY = \(\sqrt{(3 + 3) + (3 1)}\) 5 = 105, To find 8: then they are parallel. y = \(\frac{3}{2}\)x 1 Answer: Verify your answer. Now, We can say that any coincident line do not intersect at any point or intersect at 1 point Hence, All the angle measures are equal If two sides of two adjacent acute angles are perpendicular, then the angles are complementary. XY = 6.32 Explain your reasoning. Parallel to \(5x2y=4\) and passing through \((\frac{1}{5}, \frac{1}{4})\). The slope of the equation that is parallel t the given equation is: \(\frac{1}{3}\) The lines that have the same slope and different y-intercepts are Parallel lines (2) It can be observed that If you will see a tiger, then you go to the zoo-> False. We can conclude that the converse we obtained from the given statement is true Your classmate claims that no two nonvertical parallel lines can have the same y-intercept. By using the Alternate interior angles Theorem, We can conclude that the distance from point A to the given line is: 5.70, Question 5. Now, Hence, 2 and 7 are vertical angles The slope of the given line is: m = \(\frac{2}{3}\) Answer: It is given that l || m and l || n, We can conclude that the length of the field is: 320 feet, b. Hence, Now, Parallel to \(y=3\) and passing through \((2, 4)\). 8 = 180 115 10. Answer: 3x 5y = 6 The equation that is perpendicular to the given line equation is: The equation of a line is: 3 = 2 ( 0) + c The equation for another line is: -2 m2 = -1 The parallel line equation that is parallel to the given equation is: MAKING AN ARGUMENT Explain your reasoning? Answer: y = \(\frac{1}{3}\)x 4 Answer: Explain your reasoning. The given table is: Question 1. The given figure is: So, We know that, how many right angles are formed by two perpendicular lines? x = y = 61, Question 2. We can conclude that Is it possible for all eight angles formed to have the same measure? The given rectangular prism of Exploration 2 is: We know that, Slope (m) = \(\frac{y2 y1}{x2 x1}\) Answer: Find an equation of line q. Make a conjecture about how to find the coordinates of a point that lies beyond point B along \(\vec{A}\)B. Students must unlock 5 locks by: 1: determining if two given slopes are parallel, perpendicular or neither. d = \(\sqrt{(11) + (13)}\) m1 = \(\frac{1}{2}\), b1 = 1 We can observe that the product of the slopes are -1 and the y-intercepts are different y = mx + c So, Hence, from the above, 8 6 = b So, invest little times to right of entry this on-line notice Parallel And Perpendicular Lines Answer Key as capably as review them wherever you are now. a. 4 = 5 Answer: The slope of first line (m1) = \(\frac{1}{2}\) A(- 3, 2), B(5, 4); 2 to 6 Hence, from the above, = \(\frac{-1 0}{0 + 3}\) We know that, If the slope of AB and CD are the same value, then they are parallel. We can observe that the product of the slopes are -1 and the y-intercepts are different x1 = x2 = x3 . No, the third line does not necessarily be a transversal, Explanation: y = -2x + \(\frac{9}{2}\) (2) y = -2x + c x = y =29 A(15, 21), 5x + 2y = 4 We can conclude that the given statement is not correct. XY = 4.60 The y-intercept is: 9. 2 = 123 m1 m2 = \(\frac{1}{2}\) 1 = 42 = \(\frac{1}{3}\) Answer: Are the two linear equations parallel, perpendicular, or neither? Answer: x = 14 5 = c Q1: Find the slope of the line passing through the pairs of points and describe the line as rising 745 Math Consultants 8 Years on market 51631+ Customers Get Homework Help Answer: 6x = 87 Key Question: If x = 115, is it possible for y to equal 115? The given equation is: The equation of a line is: We can observe that ERROR ANALYSIS y = -3x + 19, Question 5. You decide to meet at the intersection of lines q and p. Each unit in the coordinate plane corresponds to 50 yards. 2 = 122 Using X as the center, open the compass so that it is greater than half of XP and draw an arc. You and your friend walk to school together every day. The slopes are equal fot the parallel lines Hence, Answer: A line is a circle on the sphere whose diameter is equal to the diameter of the sphere. Compare the given points with So, So, WRITING Which rays are parallel? Answer: From the given coordinate plane, Let the given points are: A (-1, 2), and B (3, -1) Compare the given points with A (x1, y1), B (x2, y2) We know that, Slope of the line (m) = \frac {y2 - y1} {x2 - x1} So, The given equation is: y = \(\frac{3}{2}\)x + c The standard form of a linear equation is: Consider the following two lines: Consider their corresponding graphs: Figure 4.6.1 The given point is: (6, 1) The Skew lines are the lines that are non-intersecting, non-parallel and non-coplanar We can observe that Hence, from the above, We know that, A(- \(\frac{1}{4}\), 5), x + 2y = 14 Hence, from the above, Hence, from the above, A(- 2, 4), B(6, 1); 3 to 2 y = mx + c P(4, 6)y = 3 m2 and m3 y = \(\frac{1}{2}\)x + 5 Answer: Explain your reasoning. Hence, from the above, We can conclude that PROBLEM-SOLVING b. 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 equation that is perpendicular to the given line equation is: We know that, The angles that have the opposite corners are called Vertical angles = 1 Now, Hence, from the above, y = -2x + 2. m = = So, slope of the given line is Question 2. The distance from the point (x, y) to the line ax + by + c = 0 is: (a) parallel to the line y = 3x 5 and 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 a) Parallel to the given line: To find the value of c, The given figure is: Answer: The given equation is: Question 39. .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. Hence, from the above, Given m1 = 115, m2 = 65 Hence, from the above, We can conclude that the parallel lines are: This contradiction means our assumption (L1 is not parallel to L2) is false, and so L1 must be parallel to L2. The representation of the Converse of the Consecutive Interior angles Theorem is: Question 2. Perpendicular lines intersect at each other at right angles 1 and 8 So, We know that, a. m5 + m4 = 180 //From the given statement = \(\frac{1}{-4}\) The given point is: A (0, 3) The sum of the adjacent angles is: 180 Slope of AB = \(\frac{1}{7}\) We can conclude that AC || DF, Question 24. m1 m2 = -1 We can conclude that the distance from point A to the given line is: 6.26. x = \(\frac{180}{2}\) Answer: In Exercises 17-22, determine which lines, if any, must be parallel. By the _______ . It is given that m || n Now, Possible answer: plane FJH 26. plane BCD 2a. Now, To find the coordinates of P, add slope to AP and PB In diagram. Parallel and Perpendicular Lines Maintaining Mathematical Proficiency Find the slope of the line. Substitute (4, -3) in the above equation The equation of a straight line is represented as y = ax + b which defines the slope and the y-intercept. 2 + 3 = 180 Hence, from the given figure, From the given figure, Given m1 = 105, find m4, m5, and m8. The Converse of the Alternate Exterior Angles Theorem: Perpendicular lines are denoted by the symbol . Example 2: State true or false using the properties of parallel and perpendicular lines. consecutive interior y = \(\frac{1}{7}\)x + 4 Justify your conclusion. We know that, Begin your preparation right away and clear the exams with utmost confidence. We know that, The slope of second line (m2) = 2 y = 3x 5 = \(\frac{8}{8}\) If so. c = 7 9 From the given figure, Now, We know that, b = 2 Question 2. These worksheets will produce 10 problems per page. A(- 9, 3), y = x 6 (5y 21) ad (6x + 32) are the alternate interior angles y = \(\frac{1}{3}\)x + \(\frac{26}{3}\) The flow proof for the Converse of Alternate exterior angles Theorem is: Answer: Question 36. By the Vertical Angles Congruence Theorem (Theorem 2.6). Hence, from the above, 2 and 4 are the alternate interior angles 8 = 65. The given pair of lines are: 1 = 2 = 42, Question 10. The given point is: A (2, -1) The given point is: A (-\(\frac{1}{4}\), 5) \(\frac{6-(-4)}{8-3}\) Hence, from the above, = 4 Answer: XY = \(\sqrt{(x2 x1) + (y2 y1)}\) We can conclude that the lines x = 4 and y = 2 are perpendicular lines, Question 6. These Parallel and Perpendicular Lines Worksheets are great for practicing identifying parallel, perpendicular, and intersecting lines from pictures. y = \(\frac{1}{2}\)x 7 The given point is: P (4, -6) The given points are: a. y = \(\frac{1}{2}\)x + b (1) y = 2x + c1 Explain your reasoning. We know that, It is given that 4 5 and \(\overline{S E}\) bisects RSF Slope (m) = \(\frac{y2 y1}{x2 x1}\) We can observe that Answer: We can conclude that the perpendicular lines are: From the given figure, Question 11. The product of the slope of the perpendicular equations is: -1 Question 33. The points are: (-9, -3), (-3, -9) According to the Vertical Angles Theorem, the vertical angles are congruent Hence, Question 13. Verticle angle theorem: 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 Hence, y = mx + c Question 16. 4 = 2 (3) + c Compare the given points with 2x + y + 18 = 180 lines intersect at 90. The equation that is parallel to the given equation is: The midpoint of PQ = (\(\frac{x1 + x2}{2}\), \(\frac{y1 + y2}{2}\)) b. Which values of a and b will ensure that the sides of the finished frame are parallel.? Answer: So, We know that, So, m1m2 = -1 3 = 47 4 and 5 are adjacent angles \(\overline{C D}\) and \(\overline{A E}\) are Skew lines because they are not intersecting and are non coplanar Hence, Answer: Answer: Perpendicular lines do not have the same slope. Slope of RS = \(\frac{-3}{-1}\) View Notes - 4.5 Equations of Parallel and Perpendicular Lines.pdf from BIO 187 at Beach High School. What are Parallel and Perpendicular Lines? x - y = 5 Areaof sphere formula Computer crash logs Data analysis statistics and probability mastery answers Direction angle of vector calculator Dividing polynomials practice problems with answers The lines that are at 90 are Perpendicular lines These guidelines, with the editor will assist you with the whole process. So, y = -3x + 150 + 500 We can say that any parallel line do not intersect at any point P = (2 + (2 / 8) 8, 6 + (2 / 8) (-6)) We can also observe that w and z is not both to x and y b) Perpendicular to the given line: The measure of 1 is 70. Answer: So, Find the distance front point A to the given line. From the given figure, Answer: The given figure is: We can conclude that So, Answer: Explain your reasoning. 3.4). Slope of ST = \(\frac{2}{-4}\) Answer: lines intersect at 90. c = \(\frac{40}{3}\) Identifying Parallel, Perpendicular, and Intersecting Lines from a Graph Perpendicular to \(xy=11\) and passing through \((6, 8)\). It is given that your classmate claims that no two nonvertical parallel lines can have the same y-intercept Answer: We can observe that the given angles are the corresponding angles Graph the equations of the lines to check that they are parallel. Hence, Hence, from the given figure, If the line cut by a transversal is parallel, then the corresponding angles are congruent = (\(\frac{8 + 0}{2}\), \(\frac{-7 + 1}{2}\)) 4 ________ b the Alternate Interior Angles Theorem (Thm. Answer: Alternate Exterior Angles Theorem (Thm. Decide whether there is enough information to prove that m || n. If so, state the theorem you would use. Answer: Question 12. The line that passes through point F that appear skew to \(\overline{E H}\) is: \(\overline{F C}\), Question 2. The standard linear equation is: Draw \(\overline{A P}\) and construct an angle 1 on n at P so that PAB and 1 are corresponding angles Justify your answer. y = mx + c In Exercises 11 and 12. find m1, m2, and m3. The product of the slopes is -1 The equation for another line is: So, = | 4 + \(\frac{1}{2}\) | We can observe that the figure is in the form of a rectangle Parallel to \(2x3y=6\) and passing through \((6, 2)\). The representation of the parallel lines in the coordinate plane is: Question 16. CONSTRUCTING VIABLE ARGUMENTS The lines that do not intersect or not parallel and non-coplanar are called Skew lines 3m2 = -1 AC is not parallel to DF. We have to find the point of intersection 8 + 115 = 180 We can conclude that the linear pair of angles is: It is given that the given angles are the alternate exterior angles ERROR ANALYSIS Answer: Question 16. Answer: The given lines are: \(m_{}=9\) and \(m_{}=\frac{1}{9}\), 13. The coordinates of line a are: (0, 2), and (-2, -2) Answer: Question 2. Is b || a? From the given figure, 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). So, Hence, from the above figure, XY = 6.32 d = | ax + by + c| /\(\sqrt{a + b}\) Proof: 2x x = 56 2 Then by the Transitive Property of Congruence (Theorem 2.2), 1 5. Justify your conjecture. Explain your reasoning. You can refer to the answers below. The Alternate Exterior Angles Theorem states that, when two parallel lines are cut by a transversal, the resulting alternate exterior angles are congruent 1 = 32. The area of the field = 320 140 The Converse of the Consecutive Interior angles Theorem: y = -2x 2 Identify all pairs of angles of the given type. y = \(\frac{1}{2}\)x 5, Question 8. We know that, The given figure is: We can observe that Hence, from the above, line(s) skew to We can conclude that b || a, Question 4. If the corresponding angles are congruent, then the two lines that cut by a transversal are parallel lines MATHEMATICAL CONNECTIONS Perpendicular lines are denoted by the symbol . Hence, from the above, In Exploration 2. m1 = 80. The given figure is: m2 = -1 HOW DO YOU SEE IT? So, c = 2 + 2 Answer: 2 = \(\frac{1}{4}\) (8) + c XZ = \(\sqrt{(7) + (1)}\) So, 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 1 = 40 then they intersect to form four right angles. We can observe that CRITICAL THINKING It is given that c = 7 Answer: b = 19 8x = 96 Q. The coordinates of line b are: (2, 3), and (0, -1) Answer: Draw an arc by using a compass with above half of the length of AB by taking the center at A above AB The following summaries about parallel and perpendicular lines maze answer key pdf will help you make more personal choices about more accurate and faster information. d = \(\sqrt{(x2 x1) + (y2 y1)}\) How would your We know that, Question 12. Explain your reasoning. Where, We can conclude that 4 and 5 are the Vertical angles. In Exercises 21 and 22, write and solve a system of linear equations to find the values of x and y. Hence, from the above, Write the equation of a line that would be parallel to this one, and pass through the point (-2, 6). x = 35 and y = 145, Question 6. For the Converse of the alternate exterior angles Theorem, We know that, In Exercises 9 and 10, trace \(\overline{A B}\). Answer: We know that, We can conclude that y = \(\frac{1}{3}\)x + c Alternate Exterior Angles Theorem: If two angles are vertical angles. We can conclude that the value of x is: 20, Question 12. c = -3 The coordinates of the quadrilateral QRST is: The coordinates of y are the same. The angles that are opposite to each other when 2 lines cross are called Vertical angles Answer: We can conclude that 2 and 11 are the Vertical angles. From the given figure, x = 107 Now, Question 4. The intersecting lines intersect each other and have different slopes and have the same y-intercept Answer: So, XY = \(\sqrt{(6) + (2)}\) The given point is: (1, 5) These Parallel and Perpendicular Lines Worksheets are great for practicing identifying perpendicular lines from pictures. Now, We can conclude that The angles that are opposite to each other when two lines cross are called Vertical angles The point of intersection = (\(\frac{3}{2}\), \(\frac{3}{2}\)) The given figure is: We can observe that we divided the total distance into the four congruent segments or pieces y = \(\frac{1}{2}\)x 3, d. y = -7x 2. Determine the slope of a line parallel to \(y=5x+3\). Then, let's go back and fill in the theorems. 1. Hence, from the above figure, Hence, from the above, What does it mean when two lines are parallel, intersecting, coincident, or skew? We know that, Question 1. 8 = 6 + b We have seen that the graph of a line is completely determined by two points or one point and its slope. How do you know that n is parallel to m? c.) Book: The two highlighted lines meet each other at 90, therefore, they are perpendicular lines. So, We can conclude that quadrilateral JKLM is a square. Identify two pairs of parallel lines so that each pair is in a different plane. m2 = 1 How do you know that the lines x = 4 and y = 2 are perpendiculars? y = 3x + c Slope of AB = \(\frac{-4 2}{5 + 3}\) Hence, from the above, Answer: Explain. We can conclude that 11 and 13 are the Consecutive interior angles, Question 18. Write the equation of the line that is perpendicular to the graph of 53x y = , and Explain why the top step is parallel t0 the ground. You are trying to cross a stream from point A. From the given figure, Compare the given points with Explain your reasoning. We can observe that there is no intersection between any bars We can conclude that the distance from point A to the given line is: 9.48, Question 6. Answer: Question 40. So, Geometry chapter 3 parallel and perpendicular lines answer key Apps can be a great way to help learners with their math. m1m2 = -1 If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent 5y = 116 + 21 Slope of QR = \(\frac{-2}{4}\) We can conclude that the equation of the line that is parallel to the line representing railway tracks is: Find an equation of line p. Question 1. Answer: Question 32. 2x + 4y = 4 The intersection point of y = 2x is: (2, 4) The standard form of the equation is: Hence, from the above, We know that, Each unit in the coordinate plane corresponds to 50 yards. m2 = \(\frac{1}{2}\), b2 = 1 The given equation is: So, From the given figure, Now, So, Hence, from the above, Determine if the lines are parallel, perpendicular, or neither. We can conclude that the consecutive interior angles of BCG are: FCA and BCA. So, The slopes of the parallel lines are the same m1 m2 = -1 Given Slope of a Line Find Slopes for Parallel and Perpendicular Lines Worksheets Answer: Question 34. Work with a partner: The figure shows a right rectangular prism. F if two coplanar strains are perpendicular to the identical line then the 2 strains are. Hence, From the given figure, -x + 4 = x 3 (2, 4); m = \(\frac{1}{2}\) If m1 = 58, then what is m2? b is the y-intercept So, Which lines intersect ? = \(\frac{6 + 4}{8 3}\) Slope of line 1 = \(\frac{-2 1}{-7 + 3}\) Alternate Interior angles theorem: Answer: So, a. (7x + 24) = 108 Therefore, these lines can be identified as perpendicular lines. Which type of line segment requires less paint? -1 = \(\frac{1}{3}\) (3) + c They are not parallel because they are intersecting each other. Write an equation of the line passing through the given point that is parallel to the given line. Question 1. If r and s are the parallel lines, then p and q are the transversals. Question 29. The given figure is: m1 = m2 = \(\frac{3}{2}\) Since k || l,by the Corresponding Angles Postulate, 1 and 5 are the alternate exterior angles c. Draw \(\overline{C D}\). Find the measures of the eight angles that are formed. So, From the figure, We can conclude that the line that is parallel to the given line equation is: Answer: forming a straight line. On the other hand, when two lines intersect each other at an angle of 90, they are known as perpendicular lines. Slope of the line (m) = \(\frac{-2 + 2}{3 + 1}\) We have to divide AB into 5 parts So, y = 2x + c We can say that The are outside lines m and n, on . 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! a. Hence, Answer: The points of intersection of intersecting lines: HOW DO YOU SEE IT? We know that, We recognize that \(y=4\) is a horizontal line and we want to find a perpendicular line passing through \((3, 2)\). y = 3x + 2, (b) perpendicular to the line y = 3x 5. Proof: The Skew lines are the lines that are not parallel, non-intersect, and non-coplanar ABSTRACT REASONING The equation for another parallel line is: x = 4 A (x1, y1), and B (x2, y2) Answer: Question 20. 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. Answer: Question 18. So, c. Consecutive Interior angles Theorem, Question 3. d = \(\sqrt{(300 200) + (500 150)}\) Slope of line 2 = \(\frac{4 + 1}{8 2}\) (1) c is the y-intercept The alternate exterior angles are: 1 and 7; 6 and 4, d. consecutive interior angles So, From the given figure, P = (3.9, 7.6) Step 6: We can conclude that 1 = 60. Consecutive Interior Angles Theorem (Thm. In Exercise 40 on page 144, We know that, Answer: Observe the horizontal lines in E and Z and the vertical lines in H, M and N to notice the parallel lines. m = 3 and c = 9 Answer: If we observe 1 and 2, then they are alternate interior angles It is given that m || n = \(\frac{1}{3}\), The slope of line c (m) = \(\frac{y2 y1}{x2 x1}\) To find the distance between the two lines, we have to find the intersection point of the line y = mx + c The lines are named as AB and CD. 2 = \(\frac{1}{2}\) (-5) + c Slope of the line (m) = \(\frac{-1 2}{3 + 1}\) y = 2x + 7. MATHEMATICAL CONNECTIONS Answer: Answer: Hence, from the above, Are the markings on the diagram enough to conclude that any lines are parallel? Answer: Identify two pairs of perpendicular lines. y = 12 The given figure is: = \(\frac{0}{4}\) The coordinates of the subway are: (500, 300) y = -2x + c Make a conjecture about what the solution(s) can tell you about whether the lines intersect. The angles formed at all the intersection points are: 90 Answer: Answer: Compare the given points with (x1, y1), (x2, y2) Alternate exterior anglesare the pair ofanglesthat lie on the outer side of the two parallel lines but on either side of the transversal line If the corresponding angles formed are congruent, then two lines l and m are cut by a transversal. 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. Explain your reasoning. The point of intersection = (0, -2) We can conclude that the pair of perpendicular lines are: In Exploration 2, Your school lies directly between your house and the movie theater. We know that, The lines that do not intersect and are not parallel and are not coplanar are Skew lines 1 = 2 (-3, 7), and (8, -6) In spherical geometry. The equation that is perpendicular to the given line equation is: You and your mom visit the shopping mall while your dad and your sister visit the aquarium. MATHEMATICAL CONNECTIONS The coordinates of line 2 are: (2, -4), (11, -6) We know that, Name two pairs of supplementary angles when \(\overline{A B}\) and \(\overline{D C}\) are parallel. = \(\frac{6 0}{0 + 2}\) The given equation is: y = \(\frac{1}{4}\)x + 4, Question 24. 2 + 10 = c b. We can observe that Answer: Question 10. From the given figure, We know that, y = x 6 -(1) According to the consecutive Interior Angles Theorem, Substitute A (6, -1) in the above equation We know that, We can conclude that there are not any parallel lines in the given figure, Question 15. E (-4, -3), G (1, 2) Now, Yes, your classmate is correct, Explanation: y = 4x 7 We know that, So, So, Where, The coordinates of the line of the second equation are: (1, 0), and (0, -2) What is m1? Now, For a pair of lines to be 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 be equal to -1 The equation of the line that is parallel to the given line equation is: c = 5 + 3 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). Hence, from the above, We can say that w and x are parallel lines by Perpendicular Transversal theorem. The given line equation is: They are not perpendicular because they are not intersecting at 90. Answer: Question 18. From the figure, The product of the slopes of the perpendicular lines is equal to -1 The given figure is: Hence, Answer: = \(\frac{2}{-6}\) 1 = 40 and 2 = 140. Hence, y = 132 Hence, from the coordinate plane, Now, So, d = \(\sqrt{(8 + 3) + (7 + 6)}\) So, When we compare the given equation with the obtained equation, We know that, Use a graphing calculator to verify your answer. Answer: Question 26. Answer: Hence, from the above, d. AB||CD // Converse of the Corresponding Angles Theorem Compare the above equation with = \(\frac{0 + 2}{-3 3}\) Hence, Hence, Question 13. The slope of PQ = \(\frac{y2 y1}{x2 x1}\) We can conclude that 18 and 23 are the adjacent angles, c.
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