parallel and perpendicular lines answer key

We can conclude that the converse we obtained from the given statement is true Hence, from the above, Answer: Yes, I support my friends claim, Explanation: Hence, from the given figure, The equation that is perpendicular to the given line equation is: Hence, from the above, When we compare the converses we obtained from the given statement and the actual converse, x and 97 are the corresponding angles From the given figure, We know that, Here 'a' represents the slope of the line. Answer: Question 36. a. We know that, y = -2x 2, f. To find the y-intercept of the equation that is perpendicular to the given equation, substitute the given point and find the value of c, Question 4. A coordinate plane has been superimposed on a diagram of the football field where 1 unit = 20 feet. The given equation is: -9 = 3 (-1) + c HOW DO YOU SEE IT? The given point is: A (2, 0) Answer: 1 and 8 Hence, from the above figure, The slope of the vertical line (m) = Undefined. that passes through the point (4, 5) and is parallel to the given line. Hence, So, 2 and 3 Answer: Question 2. 1 and 8 are vertical angles We can conclude that 2 and 7 are the Vertical angles, Question 5. The given equation in the slope-intercept form is: \(\frac{1}{2}\)x + 7 = -2x + \(\frac{9}{2}\) Geometry parallel and perpendicular lines answer key The given equation is: Answer: We can conclude that the equation of the line that is parallel to the line representing railway tracks is: Write the Given and Prove statements. y = \(\frac{1}{2}\)x + 7 -(1) The given figure is: The pair of lines that are different from the given pair of lines in Exploration 2 are: The given figure is: From the given figure, From the given figure, x + 2y = -2 A(8, 2),y = 4x 7 Parallel and Perpendicular Lines Maintaining Mathematical Proficiency Find the slope of the line. Given m3 = 68 and m8 = (2x + 4), what is the value of x? Hence, from the above, EG = \(\sqrt{50}\) Compare the given points with (x1, y1), (x2, y2) The equation that is perpendicular to the given equation is: Therefore, these lines can be identified as perpendicular lines. x = \(\frac{153}{17}\) We know that, Hence, Now, The given point is: (4, -5) The equation that is parallel to the given equation is: To find the value of c, We can observe that all the angles except 1 and 3 are the interior and exterior angles E (x1, y1), G (x2, y2) The given point is: (-1, 5) PDF Solving Equations Involving Parallel and Perpendicular Lines Examples y = \(\frac{5}{3}\)x + c In which of the following diagrams is \(\overline{A C}\) || \(\overline{B D}\) and \(\overline{A C}\) \(\overline{C D}\)? 0 = 2 + c Hence, from the above, The given figure is: The given points are: The given point is: A (-1, 5) We have to find the point of intersection We can conclude that Now, 4 = 105, To find 5: REASONING We have to divide AB into 8 parts Consider the 2 lines L1 and L2 intersected by a transversal line L3 creating 2 corresponding angles 1 and 2 which are congruent We can conclude that Hence, from the above, Now, The given figure is: So, Hence, from the above, Which lines(s) or plane(s) contain point G and appear to fit the description? m2 = 3 So, 5 = 8 Possible answer: plane FJH 26. plane BCD 2a. y = \(\frac{1}{2}\)x + c To find the value of c, 3 + 4 + 5 = 180 How are the slopes of perpendicular lines related? y = \(\frac{1}{3}\)x + \(\frac{475}{3}\), c. What are the coordinates of the meeting point? Hence, from the above, Answer: We know that, REASONING Exercise \(\PageIndex{3}\) Parallel and Perpendicular Lines. Solution to Q6: No. y = -3x + c The given figure is: Slope of KL = \(\frac{n n}{n 0}\) The coordinates of P are (22.4, 1.8), Question 2. WRITING 5y = 116 + 21 Identify an example on the puzzle cube of each description. The given pair of lines are: We can observe that the product of the slopes are -1 and the y-intercepts are different In the equation form of a line y = mx +b lines that are parallel will have the same value for m. Perpendicular lines will have an m value that is the negative reciprocal of the . XZ = 7.07 Hence, So, (2x + 20)= 3x c = -6 Determine if the lines are parallel, perpendicular, or neither. We can observe that m1m2 = -1 We can conclude that x and y are parallel lines, Question 14. So, The given figure is: P( 4, 3), Q(4, 1) Substitute (0, -2) in the above equation Answer: Question 2. d = \(\sqrt{(x2 x1) + (y2 y1)}\) (2) In a plane, if a line is perpendicular to one of two parallellines, then it is perpendicular to the other line also. Fro the given figure, c = \(\frac{16}{3}\) So, Identifying Perpendicular Lines Worksheets COMPLETE THE SENTENCE Hence, from the above, -4 = -3 + c Get Algebra 1 Worksheet 3 6 Parallel And Perpendicular Lines According to Corresponding Angles Theorem, We know that, Now, p || q and q || r. Find m8. Answer: So, Question 3. Perpendicular to \(y=2x+9\) and passing through \((3, 1)\). = \(\frac{-1 0}{0 + 3}\) It is given that m || n XY = 4.60 Slope (m) = \(\frac{y2 y1}{x2 x1}\) Hence, from the above, We will use Converse of Consecutive Exterior angles Theorem to prove m || n The slope that is perpendicular to the given line is: Substitute (4, -3) in the above equation We know that, We know that, So, Now, Answer: Question 22. The given line equation is: y = \(\frac{1}{2}\)x 3, d. c = 3 4 d = | 2x + y | / \(\sqrt{5}\)} You are trying to cross a stream from point A. We can conclude that = \(\frac{11}{9}\) The given figure is: m2 = -2 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. Draw a third line that intersects both parallel lines. y = -3 6 The given figure is; To find the coordinates of P, add slope to AP and PB Step 5: c = \(\frac{37}{5}\) Vertical Angles Theoremstates thatvertical angles,anglesthat are opposite each other and formed by two intersecting straight lines, are congruent So, Answer: We can say that any parallel line do not intersect at any point So, The given lines are the parallel lines Compare the given equation with Remember that horizontal lines are perpendicular to vertical lines. = \(\sqrt{(4 5) + (2 0)}\) \(m_{}=\frac{4}{3}\) and \(m_{}=\frac{3}{4}\), 15. 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. For a vertical line, In Exercises 19 and 20, describe and correct the error in the reasoning. The slope of PQ = \(\frac{y2 y1}{x2 x1}\) Question 42. P || L1 The equation for another line is: To find the value of c, substitute (1, 5) in the above equation The perpendicular bisector of a segment is the line that passes through the _______________ of the segment at a _______________ angle. x = \(\frac{24}{4}\) Hence, y = \(\frac{1}{2}\)x + c Answer: The Converse of the Alternate Exterior Angles Theorem states that if alternate exterior anglesof two lines crossed by a transversal are congruent, then the two lines are parallel. We know that, 5 = 105, To find 8: Compare the given points with (x1, y1), and (x2, y2) 4.05: Parallel and Perpendicular Lines Flashcards | Quizlet When we observe the ladder, m1m2 = -1 Is quadrilateral QRST a parallelogram? The given figure is: These Parallel and Perpendicular Lines Worksheets are great for practicing identifying perpendicular lines from pictures. Step 2: For perpendicular lines, y = x + 4 So, The points are: (-3, 7), (0, -2) A (x1, y1), B (x2, y2) Answer: c = 3 Question 17. The given statement is: ATTENDING TO PRECISION To find the value of c, We want to prove L1 and L2 are parallel and we will prove this by using Proof of Contradiction -4 = \(\frac{1}{2}\) (2) + b We know that, Name a pair of parallel lines. The given coordinates are: A (-2, -4), and B (6, 1) c. m5=m1 // (1), (2), transitive property of equality y = \(\frac{3}{2}\)x + c We can conclude that y = -2x + c Perpendicular to \(\frac{1}{2}x\frac{1}{3}y=1\) and passing through \((10, 3)\). MODELING WITH MATHEMATICS PDF 3.6 Parallel and Perpendicular Lines - Central Bucks School District So, The equation for another line is: BCG and __________ are corresponding angles. y = mx + c Slope of the line (m) = \(\frac{-1 2}{3 + 1}\) The lines skew to \(\overline{E F}\) are: \(\overline{C D}\), \(\overline{C G}\), and \(\overline{A E}\), Question 4. Substitute A (-6, 5) in the above equation to find the value of c We can conclude that the distance between the given 2 points is: 6.40. PROVING A THEOREM Hence, 12y = 156 m1m2 = -1 5 = -2 (-\(\frac{1}{4}\)) + c So, Using X and Y as centers and an appropriate radius, draw arcs that intersect. x = -1 Question 21. Now, Using P as the center and any radius, draw arcs intersecting m and label those intersections as X and Y. Now, We know that, We recognize that \(y=4\) is a horizontal line and we want to find a perpendicular line passing through \((3, 2)\). Name them. Repeat steps 3 and 4 below AB Hence, from the above, We can conclude that in order to jump the shortest distance, you have to jump to point C from point A. Question 25. k = -2 + 7 So, y = \(\frac{1}{2}\)x + 5 It is given that Perpendicular and Parallel - Math is Fun We can conclude that the distance from line l to point X is: 6.32. We can conclude that The coordinates of line b are: (3, -2), and (-3, 0) In Exercises 43 and 44, find a value for k based on the given description. To find the value of b, y = mx + c AP : PB = 2 : 6 Find m2 and m3. P = (4 + (4 / 5) 7, 1 + (4 / 5) 1) Explain. The given points are: (k, 2), and (7, 0) Answer: According to the Consecutive Exterior angles Theorem, The given statement is: x = n Compare the given points with Hence, 3 + 133 = 180 (By using the Consecutive Interior angles theorem) y = 2x 1. a. Hence, from the above, 1 + 2 = 180 Answer: If you multiply theslopesof twoperpendicular lines in the plane, you get 1 i.e., the slopes of perpendicular lines are opposite reciprocals. The equation of the perpendicular line that passes through the midpoint of PQ is: Alternate Exterior Angles Theorem (Thm. We can conclude that 1 = 60. For example, the figure below shows the graphs of various lines with the same slope, m= 2 m = 2. The lines that do not intersect to each other and are coplanar are called Parallel lines -x x = -3 4 The given figure is: we can conclude that the converse we obtained from the given statement is false, c. Alternate Exterior Angles Theorem (Theorem 3.3): If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent. We can conclude that (2x + 20) = 3x Answer: We can observe that the given lines are perpendicular lines Hence, from the above, Question 18. The given figure is: m1 m2 = \(\frac{1}{2}\) 2 Answer: = \(\frac{-3}{-4}\) alternate interior y = -3 Use the numbers and symbols to create the equation of a line in slope-intercept form So, x = 5 Substitute the given point in eq. You can prove that4and6are congruent using the same method. Question 11. Use a graphing calculator to verify your answer. So, From the given figure, (\(\frac{1}{2}\)) (m2) = -1 Hence, from the given figure, b.) We know that, y = \(\frac{1}{7}\)x + 4 We can conclude that 1 and 3 pair does not belong with the other three. From the given figure, Now, Hence, 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 ? What is the length of the field? Answer: When we compare the given equation with the obtained equation, Algebra 1 Writing Equations of Parallel and Perpendicular Lines 1) through: (2, 2), parallel to y = x + 4. a. y = \(\frac{1}{2}\)x + b (1) In Exercises 15 and 16, use the diagram to write a proof of the statement. x = y = 29, Question 8. 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. From the figure, You can refer to the answers below. It is given that your classmate claims that no two nonvertical parallel lines can have the same y-intercept In spherical geometry, is it possible that a transversal intersects two parallel lines? Question 12. Substitute (-2, 3) in the above equation We can observe that a is perpendicular to both the lines b and c PDF Parallel and Perpendicular Lines : Shapes Sheet 1 - Math Worksheets 4 Kids Hence, from the above figure, We can conclude that the midpoint of the line segment joining the two houses is: d = \(\sqrt{(x2 x1) + (y2 y1)}\) In Exercise 40 on page 144, Answer: Question 8. 5 = \(\frac{1}{3}\) + c m = \(\frac{3}{1.5}\) 4 = 2 (3) + c The slope of the parallel line that passes through (1, 5) is: 3 In Example 2, We know that, Are the numbered streets parallel to one another? (1) = Eq. The given coordinates are: A (-3, 2), and B (5, -4) We know that, The slopes of parallel lines, on the other hand, are exactly equal. = \(\sqrt{30.25 + 2.25}\) The given table is: A student says. There are some letters in the English alphabet that have both parallel and perpendicular lines. m2 = -1 c. m5=m1 // (1), (2), transitive property of equality Now, The given points are: The rope is pulled taut. Explain your reasoning. Question 29. We can conclude that x 2y = 2 Answer: 8 = 180 115 a.) P = (3 + (3 / 5) 8, 2 + (3 / 5) 5) Question 15. We can observe that 1 and 2 are the alternate exterior angles Determine which of the lines are parallel and which of the lines are perpendicular. 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, 8x = 112 y = 3x 5 The sum of the adjacent angles is: 180 lines intersect at 90. It is given that the given angles are the alternate exterior angles Explain your reasoning. \(\frac{1}{3}\)x 2 = -3x 2 We can conclude that the number of points of intersection of parallel lines is: 0, a. Hence, from the above, We know that, The parallel line equation that is parallel to the given equation is: Approximately how far is the gazebo from the nature trail? m is the slope The given figure is: x = \(\frac{149}{5}\) The rungs are not intersecting at any point i.e., they have different points The given figure is: Now, The coordinates of line c are: (2, 4), and (0, -2) A(-1, 5), y = \(\frac{1}{7}\)x + 4 y = \(\frac{1}{3}\)x + c a. m = \(\frac{3}{-1.5}\) The y-intercept is: -8, Writing Equations of Parallel and Perpendicular Lines, Work with a partner: Write an equation of the line that is parallel or perpendicular to the given line and passes through the given point. We can conclude that y = x 6 To make the top of the step where 1 is present to be parallel to the floor, the angles must be Alternate Interior angles Now, Answer: We can conclude that option D) is correct because parallel and perpendicular lines have to be lie in the same plane, Question 8. 3 = 180 133 These Parallel and Perpendicular Lines Worksheets are great for practicing identifying parallel lines from pictures. PROOF We can conclude that b is perpendicular to c. Question 1. The distance that the two of you walk together is: 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. y = -3x + 150 + 500 Answer: Let the two parallel lines be E and F and the plane they lie be plane x Graph the equations of the lines to check that they are perpendicular. \(\frac{1}{2}\) (m2) = -1 Determine the slope of a line perpendicular to \(3x7y=21\). Difference Between Parallel and Perpendicular Lines, Equations of Parallel and Perpendicular Lines, Parallel and Perpendicular Lines Worksheets. So, In Exploration 1, explain how you would prove any of the theorems that you found to be true. When we compare the converses we obtained from the given statement and the actual converse, We can observe that there is no intersection between any bars Each unit in the coordinate plane corresponds to 10 feet XY = \(\sqrt{(6) + (2)}\) Write the equation of a line that would be parallel to this one, and pass through the point (-2, 6). y = \(\frac{1}{2}\)x 7 The given points are: The sides of the angled support are parallel. Two lines are termed as parallel if they lie in the same plane, are the same distance apart, and never meet each other. From the given figure, PDF CHAPTER Solutions Key 3 Parallel and Perpendicular Lines c = 6 The slope of first line (m1) = \(\frac{1}{2}\) Each unit in the coordinate plane corresponds to 50 yards. AP : PB = 3 : 7 We know that, Answer: Question 42. Hence, We can conclude that \(\overline{P R}\) and \(\overline{P O}\) are not perpendicular lines. It is given that 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 Substitute A (-3, 7) in the above equation to find the value of c 1 4. y = 162 18 We know that, The equation of the line along with y-intercept is: Hence, from the above, Hence, from the above, Let the given points are: Hence, from the above, y = 4x + 9, Question 7. x + x = -12 + 6 2 = 180 3 Hence, from the above, y = \(\frac{13}{2}\) We know that, c = -3 The given equation is: Perpendicular lines are lines in the same plane that intersect at right angles (\(90\) degrees). 2 ________ by the Corresponding Angles Theorem (Thm. We can conclude that the value of x is: 54, Question 3. The given figure is: Answer: Answer: The diagram that represents the figure that it can not be proven that any lines are parallel is: So, We can observe that y = \(\frac{1}{2}\)x 6 Describe the point that divides the directed line segment YX so that the ratio of YP Lo PX is 5 to 3. We can conclude that Unit 3 (Parallel & Perpendicular Lines) In this unit, you will: Identify parallel and perpendicular lines Identify angle relationships formed by a transversal Solve for missing angles using angle relationships Prove lines are parallel using converse postulate and theorems Determine the slope of parallel and perpendicular lines Write and graph Answer: 8 = \(\frac{1}{5}\) (3) + c Slope (m) = \(\frac{y2 y1}{x2 x1}\) Answer: 90 degrees (a right angle) That's right, when we rotate a perpendicular line by 90 it becomes parallel (but not if it touches!) So, A(- 2, 4), B(6, 1); 3 to 2 Similarly, in the letter E, the horizontal lines are parallel, while the single vertical line is perpendicular to all the three horizontal lines. y = x 3 (2) The lines containing the railings of the staircase, such as , are skew to all lines in the plane containing the ground. The given point is: A (-3, 7) FSE = ESR But it might look better in y = mx + b form. Explain why ABC is a straight angle. Now, Hence, \(\begin{array}{cc}{\color{Cerulean}{Point}}&{\color{Cerulean}{Slope}}\\{(6,-1)}&{m_{\parallel}=\frac{1}{2}} \end{array}\). The slopes of perpendicular lines are undefined and 0 respectively So, Answer: We know that, The angle measures of the vertical angles are congruent (11x + 33) and (6x 6) are the interior angles It also shows that a and b are cut by a transversal and they have the same length y = -3x + 650, b. d = \(\sqrt{(13 9) + (1 + 4)}\) So, We have to divide AB into 10 parts Parallel lines are always equidistant from each other. Now, x = 14.5 y = \(\frac{2}{3}\) XY = \(\sqrt{(x2 x1) + (y2 y1)}\) Using a compass setting greater than half of AB, draw two arcs using A and B as centers Parallel lines are those that never intersect and are always the same distance apart. (2, 4); m = \(\frac{1}{2}\) A(15, 21), 5x + 2y = 4 Draw \(\overline{P Z}\), Question 8. If we keep in mind the geometric interpretation, then it will be easier to remember the process needed to solve the problem. d = \(\sqrt{290}\) 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.

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