parallel and perpendicular lines answer key

Answer: Question 26. Hence, from the above, FCA and __________ are alternate exterior angles. 7x 4x = 58 + 11 We can conclude that the distance that the two of the friends walk together is: 255 yards. Question 25. Answer: 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. To find the value of c, \(m_{}=\frac{2}{7}\) and \(m_{}=\frac{7}{2}\), 17. Compare the given points with The completed proof of the Alternate Interior Angles Converse using the diagram in Example 2 is: y = -2x + c The line that is perpendicular to y=n is: Parallel and Perpendicular Lines Perpendicular Lines Two nonvertical lines are perpendicular if their slopes are opposite reciprocals of each other. 1 7 The given lines are: The given line has the slope \(m=\frac{1}{7}\), and so \(m_{}=\frac{1}{7}\). Name them. We can say that any intersecting line do intersect at 1 point Question 16. y = -x An equation of the line representing Washington Boulevard is y = \(\frac{2}{3}\)x. Hence, from the above, Hence, from the above, Let us learn more about parallel and perpendicular lines in this article. Answer: So, The two lines are Parallel when they do not intersect each other and are coplanar 4.5 Equations of Parallel and Perpendicular Lines Solving word questions PROVING A THEOREM Perpendicular lines are intersecting lines that always meet at an angle of 90. c = 5 \(\frac{1}{2}\) The coordinates of the quadrilateral QRST is: Alternate Interior Anglesare a pair ofangleson the inner side of each of those two lines but on opposite sides of the transversal. x = 90 y = \(\frac{1}{3}\)x 2. You and your family are visiting some attractions while on vacation. Hence, Which theorem is the student trying to use? Answer: Which lines are parallel to ? We know that, The theorems involving parallel lines and transversals that the converse is true are: Now, m1m2 = -1 We can conclude that 2 and 7 are the Vertical angles, Question 5. We were asked to find the equation of a line parallel to another line passing through a certain point. From the above figure, So, Explain your reasoning. -2 = 3 (1) + c y = \(\frac{1}{7}\)x + 4 y = \(\frac{1}{3}\)x + c Cellular phones use bars like the ones shown to indicate how much signal strength a phone receives from the nearest service tower. = 3 The conjecture about \(\overline{A B}\) and \(\overline{c D}\) is: Hence, from the above, To find the value of c in the above equation, substitue (0, 5) in the above equation Hence, Answer: Question 30. From Exploration 2, We have to find the point of intersection From the given figure, Find the measure of the missing angles by using transparent paper. m = -2 Hence, from the above, Answer: Proof: x = 133 m1 = \(\frac{1}{2}\), b1 = 1 The slope of the line that is aprallle to the given line equation is: So, d = \(\sqrt{(x2 x1) + (y2 y1)}\) Answer: Answer: We can observe that Hence, The lines skew to \(\overline{Q R}\) are: \(\overline{J N}\), \(\overline{J K}\), \(\overline{K L}\), and \(\overline{L M}\), Question 4. Then use a compass and straightedge to construct the perpendicular bisector of \(\overline{A B}\), Question 10. Proof: 2 = \(\frac{1}{4}\) (8) + c We know that, On the other hand, when two lines intersect each other at an angle of 90, they are known as perpendicular lines. We know that, m = \(\frac{-2}{7 k}\) The given figure is: We know that, It is given that in spherical geometry, all points are points on the surface of a sphere. These worksheets will produce 6 problems per page. -2 = \(\frac{1}{2}\) (2) + c m2 = \(\frac{2}{3}\) The equation of the line that is parallel to the given line equation is: What conjectures can you make about perpendicular lines? Answer: c = -6 In Exercises 7 and 8, determine which of the lines are parallel and which of the lines are perpendicular. Prove the statement: If two lines are vertical. A(- \(\frac{1}{4}\), 5), x + 2y = 14 2 and 7 are vertical angles Answer: Question 24. Slope of RS = \(\frac{-3}{-1}\) Hence, Answer: Question 28. = 6.26 We can conclude that the value of x is: 90, Question 8. c = -5 Substitute A (-2, 3) in the above equation to find the value of c Draw a diagram to represent the converse. If you were to construct a rectangle, 0 = \(\frac{1}{2}\) (4) + c To find the value of b, Determine whether the converse is true. The given figure is: Answer: Answer: d = \(\sqrt{(x2 x1) + (y2 y1)}\) The equation that is perpendicular to the given line equation is: 3.12) Compare the given coordinates with Now, So, Explain your reasoning. P(- 5, 5), Q(3, 3) 12y = 156 such as , are perpendicular to the plane containing the floor of the treehouse. Let the congruent angle be P The slopes of the parallel lines are the same We can conclude that the given statement is not correct. \(\overline{D H}\) and \(\overline{F G}\) We can observe that Hence, from the above, Parallel lines We know that, If you will go to the park, then it is warm outside -> False. Answer: Answer: From the converse of the Consecutive Interior angles Theorem, P(- 7, 0), Q(1, 8) Any fraction that contains 0 in the numerator has its value equal to 0 Also, by the Vertical Angles Theorem, 4 ________ b the Alternate Interior Angles Theorem (Thm. The given figure is: We know that, Now, Question 25. Work with a partner: Write the converse of each conditional statement. x + 2y = 2 Compare the given points with (x1, y1), and (x2, y2) Answer: The slope of the parallel equations are the same Which rays are not parallel? 11y = 77 Answer: 9 and x- Answer: 2 and y Answer: x +15 and Answer: x +10 2 x -6 and 2x + 3y Answer: 6) y and 3x+y=- Answer: Answer: 14 and y = 5 6 We know that, The given figure is: In Exercises 9 and 10, trace \(\overline{A B}\). Use the diagram From the given figure, \(\frac{1}{2}\)x + 1 = -2x 1 The Coincident lines may be intersecting or parallel P = (4, 4.5) The given figure is: In Exercises 43 and 44, find a value for k based on the given description. Answer: Question 34. Yes, there is enough information to prove m || n These worksheets will produce 6 problems per page. Answer: Hence, We can conclude that 2. Identify all pairs of angles of the given type. You can select different variables to customize these Parallel and Perpendicular Lines Worksheets for your needs. Name the line(s) through point F that appear skew to . The given point is: (4, -5) If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent In spherical geometry, is it possible that a transversal intersects two parallel lines? Use a graphing calculator to verify your answer. So, Hence, To find the value of b, So, Answer: 1 = 2 If two parallel lines are cut by a transversal, then the pairs of Corresponding angles are congruent. The given figure is: We can observe that the given angles are the consecutive exterior angles The adjacent angles are: 1 and 2; 2 and 3; 3 and 4; and 4 and 1 We know that, If twolinesintersect to form a linear pair of congruent angles, then thelinesareperpendicular. The equation of the line that is perpendicular to the given line equation is: The third intersecting line can intersect at the same point that the two lines have intersected as shown below: The parallel line equation that is parallel to the given equation is: A(3, 4),y = x + 8 We can observe that It is given that m || n Hence, from the above figure, We can conclude that the given pair of lines are perpendicular lines, Question 2. Geometrically, we see that the line \(y=4x1\), shown dashed below, passes through \((1, 5)\) and is perpendicular to the given line. (7x 11) = (4x + 58) Find m2. They are always equidistant from each other. We can observe that A (x1, y1), B (x2, y2) Compare the given equation with According to the Perpendicular Transversal Theorem, The given point is: (6, 4) Classify the pairs of lines as parallel, intersecting, coincident, or skew. Here is a graphic preview for all of the Parallel and Perpendicular Lines Worksheets. CRITICAL THINKING We know that, Answer: Answer: Example 5: Tell whether the line y = {4 \over 3}x + 2 y = 34x + 2 is parallel, perpendicular or neither to the line passing through \left ( {1,1} \right) (1,1) and \left ( {10,13} \right) (10,13). Therefore, they are parallel lines. So, In Example 2, can you use the Perpendicular Postulate to show that is not perpendicular to ? Here 'a' represents the slope of the line. Substitute (-1, -1) in the above equation m1 m2 = \(\frac{1}{2}\) So, It is given that the given angles are the alternate exterior angles So, We can conclude that y = 180 35 line(s) perpendicular to . 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? AP : PB = 3 : 7 So, Now, We know that, y = \(\frac{1}{2}\)x 4, Question 22. c = 6 0 So, We can conclude that the distance between the given 2 points is: 17.02, Question 44. From the given figure, ABSTRACT REASONING It is given that 1 = 58 1 = 3 (By using the Corresponding angles theorem) Mark your diagram so that it cannot be proven that any lines are parallel. -3 = 9 + c 7x = 108 24 The coordinates of line 1 are: (10, 5), (-8, 9) You can prove that4and6are congruent using the same method. = 1 Substitute the given point in eq. Hence, So, We know that, 2x = 18 The lines that have the same slope and different y-intercepts are Parallel lines From the above figure, From the given figure, We know that, Answer: From the given figure, We can conclude that the value of x is: 60, Question 6. The slopes of the parallel lines are the same So, (- 5, 2), y = 2x 3 d = \(\sqrt{(x2 x1) + (y2 y1)}\) x = \(\frac{149}{5}\) The equation that is perpendicular to the given line equation is: Answer: Question 22. Prove: c || d We have to find 4, 5, and 8 To be proficient in math, you need to understand and use stated assumptions, definitions, and previously established results. Answer: Question 29. For example, the letter H, in which the vertical lines are parallel and the horizontal line is perpendicular to both the vertical lines. MAKING AN ARGUMENT AB = AO + OB Let the given points are: y = x \(\frac{28}{5}\) In a square, there are two pairs of parallel lines and four pairs of perpendicular lines. P = (3 + (3 / 5) 8, 2 + (3 / 5) 5) Given Slope of a Line Find Slopes for Parallel and Perpendicular Lines Worksheets y = -3x + c The given figure is: y = 2x 2. ABSTRACT REASONING WRITING We can conclue that 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. Your friend claims that because you can find the distance from a point to a line, you should be able to find the distance between any two lines. b. x = 9 y = -2x + 1, e. Hence, We know that, Answer: Question 8. m = = So, slope of the given line is Question 2. Answer: Question 48. Hence, from the coordinate plane, Parallel to \(\frac{1}{5}x\frac{1}{3}y=2\) and passing through \((15, 6)\). The equation of a straight line is represented as y = ax + b which defines the slope and the y-intercept. Follows 1 Expert Answers 1 Parallel And Perpendicular Lines Math Algebra Middle School Math 02/16/20 Slopes of Parallel and Perpendicular Lines Algebra 1 Writing Equations of Parallel and Perpendicular Lines 1) through: (2, 2), parallel to y = x + 4. We can conclude that the distance between the given lines is: \(\frac{7}{2}\). We know that, Eq. Think of each segment in the diagram as part of a line. Each unit in the coordinate plane corresponds to 10 feet. So, Answer: Perpendicular to \(y=2\) and passing through \((1, 5)\). a n, b n, and c m Now, corresponding From the given figure, consecutive interior What shape is formed by the intersections of the four lines? a is both perpendicular to b and c and b is parallel to c, Question 20. We know that, We know that, m = 2 = \(\frac{6 + 4}{8 3}\) 2 = 122, Question 16. = \(\frac{6}{2}\) The lengths of the line segments are equal i.e., AO = OB and CO = OD. Answer: (B) Alternate Interior Angles Converse (Thm 3.6) Now, We know that, In Exercises 19 and 20, describe and correct the error in the reasoning. Slope (m) = \(\frac{y2 y1}{x2 x1}\) The angles are (y + 7) and (3y 17) Identify all the pairs of vertical angles. These Parallel and Perpendicular Lines Worksheets will ask the student to find the equation of a parallel line passing through a given equation and point. Click the image to be taken to that Parallel and Perpendicular Lines Worksheet. 42 = (8x + 2) From the given figure, Find the slope of each line. Answer: y = -2 = \(\frac{5}{6}\) The equation of the line that is perpendicular to the given line equation is: The Converse of the consecutive Interior angles Theorem states that if the consecutive interior angles on the same side of a transversal line intersecting two lines are supplementary, then the two lines are parallel. Hence, from the above, When we compare the given equation with the obtained equation, 6 + 4 = 180, Question 9. We can conclude that the distance from point A to the given line is: 8.48. Substitute this slope and the given point into point-slope form. line(s) skew to . Furthermore, the rise and run between two perpendicular lines are interchanged. False, the letter A does not have a set of perpendicular lines because the intersecting lines do not meet each other at right angles. Hence, Is your friend correct? -4 = -3 + c It is given that you and your friend walk to school together every day. Answer: Compare the effectiveness of the argument in Exercise 24 on page 153 with the argument You can find the distance between any two parallel lines What flaw(s) exist in the argument(s)? The angles that have the same corner are called Adjacent angles c = 0 The given equation of the line is: 48 + y = 180 If we try to find the slope of a perpendicular line by finding the opposite reciprocal, we run into a problem: \(m_{}=\frac{1}{0}\), which is undefined. 2x = 180 Which of the following is true when are skew? Slope of line 1 = \(\frac{9 5}{-8 10}\) So, Slope of TQ = \(\frac{-3}{-1}\) We can conclude that the value of XZ is: 7.07, Find the length of \(\overline{X Y}\) Find the equation of the line passing through \((\frac{7}{2}, 1)\) and parallel to \(2x+14y=7\). Inverses Tables Table of contents Parallel Lines Example 2 Example 3 Perpendicular Lines Example 1 Example 2 Example 3 Interactive We can conclude that \(\overline{N P}\) and \(\overline{P O}\) are perpendicular lines, Question 10. 1 and 3; 2 and 4; 5 and 7; 6 and 8, b. The converse of the given statement is: We can observe that Answer: x = 4 and y = 2 Find the distance from point E to THOUGHT-PROVOKING Question 12. Now, We can conclude that A(- 2, 3), y = \(\frac{1}{2}\)x + 1 2x = 180 72 y = -2x + 8 We can conclude that the line that is parallel to the given line equation is: Hence, from the above, The slope of the given line is: m = -3 So, The conjecture about \(\overline{A O}\) and \(\overline{O B}\) is: y = -x + 8 if two lines are perpendicular to the same line. Possible answer: plane FJH plane BCD 2a. 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 . We can conclude that a || b. We know that, Hence, from the above, So, We know that, We can conclude that the distance between the meeting point and the subway is: 364.5 yards, Question 13. x + 2y = -2 (1) Question 5. So, Parallel lines are always equidistant from each other. The plane containing the floor of the treehouse is parallel to the ground. So, Explain our reasoning. Slope (m) = \(\frac{y2 y1}{x2 x1}\) A(- 2, 1), B(4, 5); 3 to 7 -3 = -4 + c Perpendicular lines are those lines that always intersect each other at right angles. A (x1, y1), and B (x2, y2) y= \(\frac{1}{3}\)x + 4 Hence, = \(\frac{45}{15}\) The area of the field = Length Width Hence, from the above, We can conclude that Answer: The given equation is: Answer: The given equation is: When two parallel lines are cut by a transversal, which of the resulting pairs of angles are congruent? So, x = 35 Hence, from the above, Geometry chapter 3 parallel and perpendicular lines answer key. (B) intersect b. So, So, 17x + 27 = 180 We have to find the point of intersection We can observe that the pair of angle when \(\overline{A D}\) and \(\overline{B C}\) are parallel is: APB and DPB, b. \(m_{}=10\) and \(m_{}=\frac{1}{10}\), Exercise \(\PageIndex{4}\) Parallel and Perpendicular Lines. The standard linear equation is: We know that, the equation that is perpendicular to the given line equation is: The representation of the parallel lines in the coordinate plane is: In Exercises 17 20. write an equation of the line passing through point P that is perpendicular to the given line. To find the value of b, x = 54 Hence, from the above, XY = \(\sqrt{(x2 x1) + (y2 y1)}\) 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. Explain. y = -3x + 650, b. Hence, from the above, Answer: Question 29. 1 + 57 = 180 The equation of the line that is parallel to the given line equation is: The product of the slopes of the perpendicular lines is equal to -1 We know that, You meet at the halfway point between your houses first and then walk to school. You and your family are visiting some attractions while on vacation. (2x + 15) = 135 The points are: (-9, -3), (-3, -9) Write an equation of the line that passes through the point (1, 5) and is So, y = 2x and y = 2x + 5 Answer: Explain your reasoning. Answer: a. Hence, Answer: So, y = 3x + 9 -(1) construction change if you were to construct a rectangle? We know that, In Exercises 13 16. write an equation of the line passing through point P that s parallel to the given line. Linear Pair Perpendicular Theorem (Thm. The product of the slopes of the perpendicular lines is equal to -1 The 2 pair of skew lines are: q and p; l and m, d. Prove that 1 2. Question 9. y = mx + c For example, AB || CD means line AB is parallel to line CD. Hence, The claim of your friend is not correct Is it possible for all eight angles formed to have the same measure? 13) y = -5x - 2 14) y = -1 G P2l0E1Q6O GKouHttad wSwoXfptiwlaer`eU yLELgCH.r C DAYlblQ wrMiWgdhstTsF wr_eNsVetrnv[eDd\.x B kMYa`dCeL nwHirtmhI KILnqfSisnBiRt`ep IGAeJokmEeCtPr[yY. Answer: Slope of the line (m) = \(\frac{y2 y1}{x2 x1}\) From the given figure, 5 = c We can conclude that the value of x is: 20, Question 12. Slope of ST = \(\frac{2}{-4}\) This can be proven by following the below steps: = \(\frac{-4}{-2}\) = 255 yards The equation that is perpendicular to the given line equation is: 5 = -2 (-\(\frac{1}{4}\)) + c 17x = 180 27 Hence, from the above, Compare the given coordinates with Answer: c = -2 k = 5 Use these steps to prove the Transitive Property of Parallel Lines Theorem y = \(\frac{1}{2}\)x + b (1) b is the y-intercept x = 147 14 Name a pair of perpendicular lines. So, Substitute A (-6, 5) in the above equation to find the value of c m2 = -1 The rope is pulled taut. m1 m2 = -1 To find the value of c, substitute (1, 5) in the above equation (E) 1 + 2 = 180 line(s) PerPendicular to . In Exercise 40 on page 144, So, E (x1, y1), G (x2, y2) THOUGHT-PROVOKING Answer: 9 = \(\frac{2}{3}\) (0) + b Now, The letter A has a set of perpendicular lines. The slope of horizontal line (m) = 0 Which point should you jump to in order to jump the shortest distance? b. m1 + m4 = 180 // Linear pair of angles are supplementary y = 2x + 12 m1m2 = -1 So, The perpendicular lines have the product of slopes equal to -1 Hence, from the above, Question 45. In the diagram, how many angles must be given to determine whether j || k? = -3 8x = (4x + 24) Answer: Identify the slope and the y-intercept of the line. We can observe that 12y 18 = 138 Alternate Interior angles are a pair of angleson the inner side of each of those two lines but on opposite sides of the transversal. The slopes of parallel lines, on the other hand, are exactly equal. 3 + 8 = 180 (11y + 19) = 96 Explain your reasoning? So, So, So, Answer: We know that, So, (2) Now, Hence, The point of intersection = (-3, -9) So, The given point is: (3, 4) Answer: Answer: We know that, Now, In Exercises 11 and 12, describe and correct the error in the statement about the diagram. Question 35. Find all the unknown angle measures in the diagram. In this case, the negative reciprocal of -4 is 1/4 and vice versa. (11x + 33) and (6x 6) are the interior angles Question 17. m2 = 3 Answer: Slope (m) = \(\frac{y2 y1}{x2 x1}\) Perpendicular lines meet at a right angle. The equation of a line is x + 2y = 10. We can conclude that the midpoint of the line segment joining the two houses is: We know that, A (-2, 2), and B (-3, -1) Answer: x1 = x2 = x3 . 3.4) Answer: Label the point of intersection as Z. From y = 2x + 5, y = -2x + c lines intersect at 90. So, y = mx + b So, Hence, Question 39. Answer: Now, Answer: No, p ||q and r ||s will not be possible at the same time because when p || q, r, and s can act as transversal and when r || s, p, and q can act as transversal. In Exploration 2. m1 = 80. a. The Skew lines are the lines that are non-intersecting, non-parallel and non-coplanar Now, By using the Alternate interior angles Theorem, When we compare the converses we obtained from the given statement and the actual converse, Now, a = 2, and b = 1 We can observe that, We have to prove that m || n The rungs are not intersecting at any point i.e., they have different points Now, From the given figure, To find the value of c, Notice that the slope is the same as the given line, but the \(y\)-intercept is different. Select all that apply. CONSTRUCTING VIABLE ARGUMENTS Perpendicular lines are lines in the same plane that intersect at right angles (\(90\) degrees). So, Click here for More Geometry Worksheets The coordinates of x are the same. We can conclude that \(\overline{P R}\) and \(\overline{P O}\) are not perpendicular lines. So, -2 = \(\frac{1}{3}\) (-2) + c b. m1 + m4 = 180 // Linear pair of angles are supplementary You are designing a box like the one shown. If the corresponding angles are congruent, then the lines cut by a transversal are parallel Hence, from the above, No, the third line does not necessarily be a transversal, Explanation: transv. Chapter 3 Parallel and Perpendicular Lines Key. Question 1. = \(\frac{10}{5}\) We can conclude that 11 and 13 are the Consecutive interior angles, Question 18. FCJ and __________ are alternate interior angles. In a plane, if a line is perpendicular to one of two parallellines, then it is perpendicular to the other line also. Line 1: (- 3, 1), (- 7, 2) The coordinates of P are (3.9, 7.6), Question 3. Answer: AC is not parallel to DF. 2x = 135 15 m2 = \(\frac{1}{2}\), b2 = 1 We know that, Let the two parallel lines that are parallel to the same line be G AP : PB = 3 : 2 b. Question 4. Hence, from the above, So, The given coordinates are: A (-2, -4), and B (6, 1) Answer: Question 12. From the given figure, In Exercises 21-24. are and parallel? Answer: If the slopes of the opposite sides of the quadrilateral are equal, then it is called as Parallelogram d = 32 y = mx + c x = n Answer: (50, 500), (200, 50) THINK AND DISCUSS 1. We can conclude that it is not possible that a transversal intersects two parallel lines. Each unit in the coordinate plane corresponds to 10 feet Observe the horizontal lines in E and Z and the vertical lines in H, M and N to notice the parallel lines. So, Now, So, So, The given point is: (1, 5) y = -x 12 (2) c. m5=m1 // (1), (2), transitive property of equality The given figure is: Now, The equation of the line that is perpendicular to the given line equation is: line(s) perpendicular to If a || b and b || c, then a || c 3.3). We can observe that y = -9 Hence, from the above, A (-1, 2), and B (3, -1) We can conclude that 1 and 5 are the adjacent angles, Question 4. The given equation is: Substitute A (-9, -3) in the above equation to find the value of c The given equations are: If not, what other information is needed? Answer: Question 2. y = 3x + 9 (-3, 7), and (8, -6) The opposite sides of a rectangle are parallel lines. Prove 2 4 For example, if the equation of two lines is given as, y = 1/5x + 3 and y = - 5x + 2, we can see that the slope of one line is the negative reciprocal of the other. Hence, = \(\frac{325 175}{500 50}\) If p and q are the parallel lines, then r and s are the transversals Answer: Question 18. The given figure is: y = 2x + c Use the photo to decide whether the statement is true or false. Bertha Dr. is parallel to Charles St. These Parallel and Perpendicular Lines Worksheets will give the student a pair of equations for lines and ask them to determine if the lines are parallel, perpendicular, or intersecting. = 0 Answer: The coordinates of line 2 are: (2, -4), (11, -6) Answer: Question 26. Now, Alternate Exterior Angles Theorem: In Exercises 5-8, trace line m and point P. Then use a compass and straightedge to construct a line perpendicular to line m through point P. Question 6. We can conclude that, The opposite sides are parallel and the intersecting lines are perpendicular. The given figure is: m1 and m5 From the given figure, We know that, A (x1, y1), B (x2, y2) y = \(\frac{1}{3}\)x 4 Answer: In Exercises 3-8. find the value of x that makes m || n. Explain your reasoning. Lines Perpendicular to a Transversal Theorem (Theorem 3.12): In a plane. alternate interior If we draw the line perpendicular to the given horizontal line, the result is a vertical line. ATTENDING TO PRECISION Answer: From the slopes, Question 1. Hence, from the above, Compare the given points with From the given figure, Is she correct? a. Question 1. Explain your reasoning. Hence, from the above, x = 180 73 The points are: (0, 5), and (2, 4) y = mx + c 8 = -2 (-3) + b Answer: Hence, We can conclude that the value of the given expression is: 2, Question 36. Now, By comparing the given pair of lines with 3m2 = -1 From the argument in Exercise 24 on page 153, We know that, So, XY = \(\sqrt{(6) + (2)}\) So, The equation that is parallel to the given equation is: i.e., Answer: So, answer choices Parallel Perpendicular Neither Tags: MGSE9-12.G.GPE.5 Question 7 300 seconds We can say that any coincident line do not intersect at any point or intersect at 1 point Question 1. 2 = 180 123 We can observe that The given perpendicular line equations are: The slope of PQ = \(\frac{y2 y1}{x2 x1}\) We know that, The slope is: 3 y = \(\frac{1}{2}\)x + 2 3m2 = -1 So, Answer: Question 50. The given point is: A (3, -1) Question 5. d = \(\sqrt{(x2 x1) + (y2 y1)}\) The distance wont be in negative value, Question 47. Enter a statement or reason in each blank to complete the two-column proof. c = 0 2 So, = 1 2 and 3 are the congruent alternate interior angles, Question 1. Hence, Question: What is the difference between perpendicular and parallel? In Exercises 9 12, tell whether the lines through the given points are parallel, perpendicular, or neither. We know that, = \(\sqrt{(3 / 2) + (3 / 2)}\) So, Answer: Compare the given points with (x1, y1), and (x2, y2) y = -3x + 650 x = y =29 Then explain how your diagram would need to change in order to prove that lines are parallel. Hence,f rom the above, 132 = (5x 17) Answer: The points of intersection of intersecting lines: Answer: Question 4. Examine the given road map to identify parallel and perpendicular streets. The area of the field = 320 140 It is given that m || n So, 3y = x + 475 Answer: Prove: t l. PROOF From the given figure, Are the markings on the diagram enough to conclude that any lines are parallel? The slope of the perpendicular line that passes through (1, 5) is: \(\frac{5}{2}\)x = 5 What is the perimeter of the field? y = \(\frac{1}{4}\)x 7, Question 9. Is your classmate correct? Line 1: (1, 0), (7, 4) 1 = 42 20 = 3x 2x Now, The lines that are at 90 are Perpendicular lines Decide whether it is true or false. A(1, 3), B(8, 4); 4 to 1 The distance between lines c and d is y meters. 1. Look at the diagram in Example 1. So, HOW DO YOU SEE IT? Compare the given equation with Draw an arc by using a compass with above half of the length of AB by taking the center at A above AB

parallel and perpendicular lines answer key 2023