x y = -4 Parallel and Perpendicular Lines From the given slopes of the lines, identify whether the two lines are parallel, perpendicular, or neither. 1 and 8 are vertical angles y = -2x 2 The intersection point of y = 2x is: (2, 4) Slope of AB = \(\frac{1 + 4}{6 + 2}\) MATHEMATICAL CONNECTIONS For a pair of lines to be coincident, the pair of lines have the same slope and the same y-intercept Answer: We can conclude that the alternate interior angles are: 4 and 5; 3 and 6, Question 14. We have to find the point of intersection c = -6 The coordinates of P are (7.8, 5). So, We can observe that there are 2 pairs of skew lines Given: 1 and 3 are supplementary Hence, b. y = \(\frac{1}{2}\)x 2 m = \(\frac{-2}{7 k}\) y = \(\frac{3}{2}\)x 1 Answer: The Skew lines are the lines that are not parallel, non-intersect, and non-coplanar We can observe that 1 = 123 and 2 = 57. Answer: ATTENDING TO PRECISION We know that, So, MATHEMATICAL CONNECTIONS The product of the slopes of the perpendicular lines is equal to -1 For a vertical line, i.e., So, Hence, from the above, The Corresponding Angles Postulate states that, when two parallel lines are cut by a transversal, the resulting corresponding anglesare congruent We can conclude that \(\overline{K L}\), \(\overline{L M}\), and \(\overline{L S}\), d. Should you have named all the lines on the cube in parts (a)-(c) except \(\overline{N Q}\)? Prove m||n (B) intersect Here is a quick review of the point/slope form of a line. Question 1. The slope of the given line is: m = \(\frac{1}{2}\) Now, Answer: We can observe that 35 and y are the consecutive interior angles Identify all the pairs of vertical angles. We know that, The are outside lines m and n, on . c. Consecutive Interior angles Theorem, Question 3. We can conclude that the parallel lines are: x = \(\frac{84}{7}\) The given equation is: So, These Parallel and Perpendicular Lines Worksheets are a great resource for children in the 5th Grade, 6th Grade, 7th Grade, 8th Grade, 9th Grade, and 10th Grade. b. From y = 2x + 5, We can conclude that Answer: The equation of the line that is perpendicular to the given line equation is: = 2, The slope of line b (m) = \(\frac{y2 y1}{x2 x1}\) Answer: Question 16. Answer: So, so they cannot be on the same plane. Your school is installing new turf on the football held. COMPLETE THE SENTENCE We can conclude that the distance from point X to \(\overline{W Z}\) is: 6.32, Find XZ Alternate Exterior Angles Theorem: Answer: y = -2x + 8 (A) Corresponding Angles Converse (Thm 3.5) The points are: (0, 5), and (2, 4) The given pair of lines are: According to the Consecutive Exterior angles Theorem, Hence, \(\frac{8-(-3)}{7-(-2)}\) So, Possible answer: plane FJH plane BCD 2a. So, Lines Perpendicular to a Transversal Theorem (Thm. = 2 Substitute A (-3, 7) in the above equation to find the value of c The given figure is: Hence, from the above, We can conclude that the distance between the meeting point and the subway is: 364.5 yards, Question 13. REASONING The product of the slopes of the perpendicular lines is equal to -1 Prove 1, 2, 3, and 4 are right angles. y 500 = -3x + 150 We can conclude that the pair of skew lines are: We can conclude that the pair of perpendicular lines are: Answer: The Converse of Corresponding Angles Theorem: There are many shapes around us that have parallel and perpendicular lines in them. The given point is: P (4, 0) 1 + 2 = 180 Slope of MJ = \(\frac{0 0}{n 0}\) 1 = 80 Hence, from the above, In Exercises 11 and 12, describe and correct the error in the statement about the diagram. Now, The representation of the parallel lines in the coordinate plane is: Question 16. (A) are parallel. ERROR ANALYSIS Hence, from the above, For example, the figure below shows the graphs of various lines with the same slope, m= 2 m = 2. 8 = 65 1 + 57 = 180 When we observe the ladder, To use the "Parallel and Perpendicular Lines Worksheet (with Answer Key)" use the clues in identifying whether two lines are parallel or perpendicular with each other using the slope. and N(4, 1), Is the triangle a right triangle? Name the line(s) through point F that appear skew to . The given figure shows that angles 1 and 2 are Consecutive Interior angles y = 3x 5 Explain your reasoning. Answer: We know that, We can conclude that the distance from the given point to the given line is: 32, Question 7. Answer: Answer: Write the equation of a line that would be parallel to this one, and pass through the point (-2, 6). = \(\sqrt{(4 5) + (2 0)}\) Explain your reasoning. Each bar is parallel to the bar directly next to it. i.e., (a) parallel to and Hence, Justify your answer. When we unfold the paper and examine the four angles formed by the two creases, we can conclude that the four angles formed are the right angles i.e., 90, Work with a partner. So, We can observe that the length of all the line segments are equal 3 = 68 and 8 = (2x + 4) We can observe that Hence, from the above, Find the value of x that makes p || q. We can conclude that the distance between the given 2 points is: 17.02, Question 44. m2 = 2 x = 97, Question 7. The given point is: P (-8, 0) The given figure is: = \(\sqrt{(-2 7) + (0 + 3)}\) Write an equation for a line parallel to y = 1/3x - 3 through (4, 4) Q. If so, dont bother as you will get a complete idea through our BIM Geometry Chapter 3 Parallel and Perpendicular Lines Answer Key. y = mx + b The given points are: P (-7, 0), Q (1, 8) The given equation is: 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). c = 4 3 The representation of the given point in the coordinate plane is: Question 54. Possible answer: plane FJH 26. plane BCD 2a. y = \(\frac{1}{3}\) (10) 4 The given equation is:, If the corresponding angles are congruent, then the two lines that cut by a transversal are parallel lines 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. = 2.23 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, We can conclude that x = 12 So, (C) are perpendicular Think of each segment in the figure as part of a line. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. We know that, c. m5=m1 // (1), (2), transitive property of equality If both pairs of opposite sides of a quadrilateral are parallel, then it is a parallelogram MODELING WITH MATHEMATICS Question 39. Find an equation of the line representing the new road. Let the congruent angle be P We can conclude that The slope is: \(\frac{1}{6}\) We can conclude that the school have enough money to purchase new turf for the entire field. Answer: b. The given figure is; (C) Alternate Exterior Angles Converse (Thm 3.7) The equation of the parallel line that passes through (1, 5) is: The distance from the point (x, y) to the line ax + by + c = 0 is: Now, By comparing the slopes, XZ = 7.07 Can you find the distance from a line to a plane? Find m1. We know that, ATTENDING TO PRECISION 9 = \(\frac{2}{3}\) (0) + b y = \(\frac{1}{5}\)x + c The given figure is: Answer: We know that, In Exercises 47 and 48, use the slopes of lines to write a paragraph proof of the theorem. Mark your diagram so that it cannot be proven that any lines are parallel. Answer: The equation that is perpendicular to the given equation is: We use this and the point \((\frac{7}{2}, 1)\) in point-slope form. Similarly, in the letter E, the horizontal lines are parallel, while the single vertical line is perpendicular to all the three horizontal lines. The lines that have the same slope and different y-intercepts are Parallel lines We know that, We know that, We can conclude that the linear pair of angles is: Line c and Line d are parallel lines m1m2 = -1 We can conclue that y = \(\frac{1}{4}\)x + c y = \(\frac{1}{4}\)x 7, Question 9. 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: One way to build stairs is to attach triangular blocks to angled support, as shown. To find the value of c, Answer: Question 30. We know that, Answer: Hence, from the above, 10. What is the relationship between the slopes? Where, We know that, So, Draw \(\overline{A B}\), as shown. m = \(\frac{-30}{15}\) 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 ? y = mx + b Lines l and m are parallel. The equation of the line along with y-intercept is: Slope (m) = \(\frac{y2 y1}{x2 x1}\) The coordinates of the meeting point are: (150. Find the Equation of a Perpendicular Line Passing Through a Given Equation and Point -5 = 2 (4) + c Write an equation of the line passing through the given point that is parallel to the given line. Hence, If you go to the zoo, then you will see a tiger From the given figure, We know that, We can conclude that x and y are parallel lines, Question 14. m = 2 \(\overline{C D}\) and \(\overline{E F}\), d. a pair of congruent corresponding angles 2-4 Additional Practice Parallel And Perpendicular Lines Answer Key November 7, 2022 admin 2-4 Extra Observe Parallel And Perpendicular Strains Reply Key. y = -2x + c The slope of the parallel line that passes through (1, 5) is: 3 \(\frac{1}{2}\)x + 1 = -2x 1 if two lines are perpendicular to the same line. Find the equation of the line perpendicular to \(x3y=9\) and passing through \((\frac{1}{2}, 2)\). 42 and (8x + 2) are the vertical angles We know that, So, Answer: Question 4. We can conclude that the values of x and y are: 9 and 14 respectively. Answer: From the given figure, 6-3 Write Equations of Parallel and Perpendicular Lines Worksheet. If two parallel lines are cut by a transversal, then the pairs of Alternate exterior angles are congruent. If you multiply theslopesof twoperpendicular lines in the plane, you get 1 i.e., the slopes of perpendicular lines are opposite reciprocals. So, Answer: b. Unfold the paper and examine the four angles formed by the two creases. (1) The slopes are equal fot the parallel lines Answer: So, So, then they are parallel. Justify your answer. Is b c? 1 = 2 (By using the Vertical Angles theorem) P(- 7, 0), Q(1, 8) We can conclude that Given a Pair of Lines Determine if the Lines are Parallel, Perpendicular, or Intersecting -5 2 = b In Exercises 27-30. find the midpoint of \(\overline{P Q}\). Hence, y = -3x + 650, b. The product of the slopes of the perpendicular lines is equal to -1 Question 9. The slope of line a (m) = \(\frac{y2 y1}{x2 x1}\) M = (150, 250), b. The given figure is: Is quadrilateral QRST a parallelogram? We can conclude that Write the equation of the line that is perpendicular to the graph of 9y = 4x , and whose y-intercept is (0, 3). The product of the slopes of the perpendicular lines is equal to -1 So, We can conclude that The slopes of the parallel lines are the same The equation of the line along with y-intercept is: x = 97 If it is warm outside, then we will go to the park These worksheets will produce 6 problems per page. We know that, So, Is your classmate correct? 2. To find the coordinates of P, add slope to AP and PB Hence, from the above, 2y and 58 are the alternate interior angles 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 Hence, from the above, According to the consecutive exterior angles theorem, Hence, Compare the given coordinates with We know that, x || y is proved by the Lines parallel to Transversal Theorem. The 2 pair of skew lines are: q and p; l and m, d. Prove that 1 2. y = \(\frac{1}{2}\)x 5, Question 8. We know that, EG = \(\sqrt{(1 + 4) + (2 + 3)}\) PDF Name: Unit 3: Parallel & Perpendicular Lines Bell: Homework 5: Linear. x = 4 and y = 2 We know that, Hence, from the above, m2 = \(\frac{2}{3}\) Answer: Identify the slope and the y-intercept of the line.

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