x + 2y = 10 w y and z x Answer: Explain your reasoning. The width of the field is: 140 feet Question 31. Question 37. The sides of the angled support are parallel. Is your friend correct? Answer: Question 14. We know that, 9 0 = b According to Alternate interior angle theorem, Answer: Explain why the top rung is parallel to the bottom rung. Tell which theorem you use in each case. Here you get + 1 +1 and not - 1 1, so these lines are not perpendicular either. d = \(\sqrt{(300 200) + (500 150)}\) (\(\frac{1}{3}\)) (m2) = -1 Answer: Question 28. So, According to the Transitive Property of parallel lines, We know that, The coordinates of the school = (400, 300) m = \(\frac{5}{3}\) If two parallel lines are cut by a transversal, then the pairs of Corresponding angles are congruent. If a || b and b || c, then a || c The given line equation is: y = -x, Question 30. For perpendicular lines, So, Algebra 1 Parallel and Perpendicular lines What is the equation of the line written in slope-intercept form that passes through the point (-2, 3) and is parallel to the line y = 3x + 5? We can observe that the product of the slopes are -1 and the y-intercepts are different All the angles are right angles. XY = \(\sqrt{(3 + 1.5) + (3 2)}\) 2 6, c. 1 ________ by the Alternate Exterior Angles Theorem (Thm. In Exercises 43 and 44, find a value for k based on the given description. From the given figure, Equations of Parallel and Perpendicular Lines - ChiliMath PDF 3.6 Parallel and Perpendicular Lines - Central Bucks School District To prove: l || k. Question 4. The lines that are at 90 are Perpendicular lines Do you support your friends claim? We can observe that 180 = x + x So, 1 = 4 Hence, then they intersect to form four right angles. Hence, By comparing the slopes, 4 = 5 Question 21. Now, The slopes of the parallel lines are the same According to Corresponding Angles Theorem, Substitute A (8, 2) in the above equation Slope (m) = \(\frac{y2 y1}{x2 x1}\) The representation of the given pair of lines in the coordinate plane is: From the given figure, We can observe that the given angles are consecutive exterior angles 6.3 Equations in Parallel/Perpendicular Form - Algebra They are always equidistant from each other. Answer: Question 12. The coordinates of line b are: (2, 3), and (0, -1) m2 = 3 Hence, If two sides of two adjacent acute angles are perpendicular, then the angles are complementary. 4 = 2 (3) + c Thus the slope of any line parallel to the given line must be the same, \(m_{}=5\). So, y = mx + c The equation that is perpendicular to the given line equation is: x = 35 Answer: Hence, y = (5x 17) Answer: Hence, from the above, 2 = 41 1 and 3 are the vertical angles From y = 2x + 5, y = -2x So, Answer: The missing information the student assuming from the diagram is: y = -2x + 1 Hence, from the above, d = | 2x + y | / \(\sqrt{2 + (1)}\) Explain our reasoning. Line 1: (- 9, 3), (- 5, 7) Find the distance from the point (- 1, 6) to the line y = 2x. Find an equation of the line representing the new road. c = 6 Is your classmate correct? 0 = 3 (2) + c Measure the lengths of the midpoint of AB i.e., AD and DB. We can conclude that the values of x and y are: 9 and 14 respectively. We know that, The representation of the given pair of lines in the coordinate plane is: Use the diagram We can observe that there are 2 perpendicular lines Substitute A (-1, 5) in the above equation Parallel lines are always equidistant from each other. = \(\frac{2}{-6}\) Enter your answer in the box y=2/5x2 For which of the theorems involving parallel lines and transversals is the converse true? ABSTRACT REASONING Now, (b) perpendicular to the given line. We can conclude that the distance between the given 2 points is: 6.40. Question 5. So, So, Then explain how your diagram would need to change in order to prove that lines are parallel. The resultant diagram is: We know that, So, b.) We know that, We can conclude that the distance between the meeting point and the subway is: 364.5 yards, Question 13. 1 = 2 = 42, Question 10. 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. Classify the pairs of lines as parallel, intersecting, coincident, or skew. We know that, Answer: This can be proven by following the below steps: = \(\sqrt{(3 / 2) + (3 / 4)}\) NAME _____ DATE _____ PERIOD _____ Chapter 4 26 Glencoe Algebra 1 4-4 Skills Practice Parallel and Perpendicular Lines In Example 4, the given theorem is Alternate interior angle theorem We know that, Answer: We can conclude that the lines that intersect \(\overline{N Q}\) are: \(\overline{N K}\), \(\overline{N M}\), and \(\overline{Q P}\), c. Which lines are skew to ? Answer: Use the diagram to find the measure of all the angles. The given figure is: The plane containing the floor of the treehouse is parallel to the ground. From the given figure, 3. Explain your reasoning. Parallel, Intersecting, and Perpendicular Lines Worksheets y = \(\frac{1}{2}\)x \(\frac{1}{2}\), Question 10. Hence, from the above, x = 14.5 and y = 27.4, Question 9. m = -2 Which point should you jump to in order to jump the shortest distance? We can conclude that the third line does not need to be a transversal. The product of the slopes of the perpendicular lines is equal to -1 In Exercises 15 and 16, prove the theorem. = 2 (320 + 140) So, Now, We know that, Perpendicular and Parallel - Math is Fun Hence, from the above, Answer: Question 16. So, We can conclude that Use the results of Exploration 1 to write conjectures about the following pairs of angles formed by two parallel lines and a transversal. How can you write an equation of a line that is parallel or perpendicular to a given line and passes through a given point? We know that, We can conclude that in order to jump the shortest distance, you have to jump to point C from point A. m || n is true only when 3x and (2x + 20) are the corresponding angles by using the Converse of the Corresponding Angles Theorem Perpendicular to \(x=\frac{1}{5}\) and passing through \((5, 3)\). A triangle has vertices L(0, 6), M(5, 8). We know that, c = 5 \(\frac{1}{2}\) The slope that is perpendicular to the given line is: 3x = 69 So, what Given and Prove statements would you use? If so, dont bother as you will get a complete idea through our BIM Geometry Chapter 3 Parallel and Perpendicular Lines Answer Key. We know that, Slope of the line (m) = \(\frac{-1 2}{-3 + 2}\) XY = 6.32 Compare the given coordinates with 1 = 2 y = mx + b So, ABSTRACT REASONING Hence, it can be said that if the slope of two lines is the same, they are identified as parallel lines, whereas, if the slope of two given lines are negative reciprocals of each other, they are identified as perpendicular lines. Using X as the center, open the compass so that it is greater than half of XP and draw an arc. You started solving the problem by considering the 2 lines parallel and two lines as transversals 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. Hence, y = -2x + c y = x + c So, 1 = 40 m = \(\frac{-30}{15}\) A line is a circle on the sphere whose diameter is equal to the diameter of the sphere. AP : PB = 3 : 2 The parallel line equation that is parallel to the given equation is: 2x + y + 18 = 180 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. We can conclude that Parallel and perpendicular lines are an important part of geometry and they have distinct characteristics that help to identify them easily. A (x1, y1), B (x2, y2) Now, CRITICAL THINKING We know that, k = 5 d = \(\sqrt{(x2 x1) + (y2 y1)}\) Answer: Hence, The points of intersection of parallel lines: Substitute the given point in eq. Find the distance from the point (6, 4) to the line y = x + 4. So, Hence, from the above, 140 21 32 = 6x Answer: THINK AND DISCUSS 1. COMPLETE THE SENTENCE Slope (m) = \(\frac{y2 y1}{x2 x1}\) 3 + 4 = c Hence, c = -1 1 Answer: We know that, d = \(\sqrt{(x2 x1) + (y2 y1)}\) The slope of first line (m1) = \(\frac{1}{2}\) The line through (k, 2) and (7, 0) is perpendicular to the line y = x \(\frac{28}{5}\). If the slopes of two distinct nonvertical lines are equal, the lines are parallel. 2x = 7 You are trying to cross a stream from point A. Answer: Question 40. Answer: So, Answer: We can conclude that the line that is perpendicular to \(\overline{C D}\) is: \(\overline{A D}\) and \(\overline{C B}\), Question 6. Question 37. Determine the slope of a line perpendicular to \(3x7y=21\). Follows 1 Expert Answers 1 Parallel And Perpendicular Lines Math Algebra Middle School Math 02/16/20 Slopes of Parallel and Perpendicular Lines x = 3 (2) AP : PB = 2 : 6 The equation of the line that is perpendicular to the given line equation is: The letter A has a set of perpendicular lines. Use the photo to decide whether the statement is true or false. Answer: Hence, We know that, The rungs are not intersecting at any point i.e., they have different points Line 1: (10, 5), (- 8, 9) So, Hence, from the above, The equation of the line that is parallel to the given line equation is: Any fraction that contains 0 in the numerator has its value equal to 0 The given figure is: Example 2: State true or false using the properties of parallel and perpendicular lines. k 7 = -2 The slopes are equal fot the parallel lines The claim of your friend is not correct Explain our reasoning. Find a formula for the distance from the point (x0, Y0) to the line ax + by = 0. The given coordinates are: A (-3, 2), and B (5, -4) i.e., Alternate exterior angles are the pair of anglesthat lie on the outer side of the two parallel lines but on either side of the transversal line. If two lines x and y are horizontal lines and they are cut by a vertical transversal z, then 8 = 65 So, m1m2 = -1 Hence, y = \(\frac{1}{2}\)x + 7 -(1) y = 3x + c A (x1, y1), and B (x2, y2) From the given figure, We can conclude that 8 right angles are formed by two perpendicular lines in spherical geometry. = \(\frac{8}{8}\) A coordinate plane has been superimposed on a diagram of the football field where 1 unit = 20 feet. The line l is also perpendicular to the line j Show your steps. Answer: By using the Alternate Exterior Angles Theorem, Hence, Slope of Parallel and Perpendicular Lines Worksheets Compare the given points with We can observe that the given lines are parallel lines Solving Equations Involving Parallel and Perpendicular Lines www.BeaconLC.org2001 September 22, 2001 9 Solving Equations Involving Parallel and Perpendicular Lines Worksheet Key Find the slope of a line that is parallel and the slope of a line that is perpendicular to each line whose equation is given. The product of the slopes of perpendicular lines is equal to -1 2y + 4x = 180 Verify your formula using a point and a line. Answer: In Exercises 17-22, determine which lines, if any, must be parallel. From the above table, Hence, from the above, ERROR ANALYSIS Compare the given points with 1 = 2 The given equations are: In the parallel lines, We know that, Answer: We know that, Slope of line 1 = \(\frac{9 5}{-8 10}\) If the pairs of alternate interior angles are, Answer: The angles that have the common side are called Adjacent angles So, Given 1 3 In Exercises 9 12, tell whether the lines through the given points are parallel, perpendicular, or neither. Answer: The Converse of the Consecutive Interior angles Theorem: Now, The product of the slopes is -1 Explain your reasoning. -x x = -3 4 68 + (2x + 4) = 180 2 = \(\frac{1}{2}\) (-5) + c THOUGHT-PROVOKING 9 = \(\frac{2}{3}\) (0) + b Answer: Question 14. So, To be proficient in math, you need to understand and use stated assumptions, definitions, and previously established results. P(0, 0), y = 9x 1 WHAT IF? b. a. The symbol || is used to represent parallel lines. ERROR ANALYSIS d = \(\sqrt{(x2 x1) + (y2 y1)}\) So, So, Answer: For a square, Question 15. Verticle angle theorem: The are outside lines m and n, on . Now, The given points are: y = \(\frac{1}{2}\)x + c The corresponding angles are: and 5; 4 and 8, b. alternate interior angles 12y = 138 + 18 We can conclude that 44 and 136 are the adjacent angles, b. Draw \(\overline{P Z}\), Question 8. The given statement is: 1 8 For example, if given a slope. If parallel lines are cut by a transversal line, thenconsecutive exterior anglesare supplementary. The angle measures of the vertical angles are congruent y = \(\frac{1}{4}\)x + c The representation of the complete figure is: PROVING A THEOREM Given m1 = 115, m2 = 65 Justify your answer. So, We know that, d = \(\sqrt{(8 + 3) + (7 + 6)}\) m is the slope In exercises 25-28. copy and complete the statement. c = 5 7 In a plane, if a line is perpendicular to one of two parallellines, then it is perpendicular to the other line also. The given equation in the slope-intercept form is: By comparing the given pair of lines with y = 7 State which theorem(s) you used. Slope of AB = \(\frac{5}{8}\) We can conclude that p and q; r and s are the pairs of parallel lines. = 44,800 square feet y = -2 (-1) + \(\frac{9}{2}\) The diagram of the control bar of the kite shows the angles formed between the Control bar and the kite lines. 1 = 53.7 and 5 = 53.7 We can conclude that it is not possible that a transversal intersects two parallel lines. To find the value of c, We can conclude that 1 2. justify your answer. Hence, from the above, Slope of RS = \(\frac{-3}{-1}\) Hence, from the above, Answer: The Corresponding Angles Postulate states that, when two parallel lines are cut by a transversal, the resulting corresponding anglesare congruent 2x y = 18 So, b. We can observe that a is perpendicular to both the lines b and c A(- 2, 4), B(6, 1); 3 to 2 The given equation in the slope-intercept form is: PDF Parallel and Perpendicular lines - School District 43 Coquitlam

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