parallel and perpendicular lines answer key parallel and perpendicular lines answer key

Answer: For the intersection point of y = 2x, The equation that is parallel to the given equation is: It is given that 4 5. Hence, from the above, Given a Pair of Lines Determine if the Lines are Parallel, Perpendicular, or Intersecting Answer: Question 20. Answer: Hence, from he above, The map shows part of Denser, Colorado, Use the markings on the map. 4.7 of 5 (20 votes) Fill PDF Online Download PDF. The Converse of the Alternate Exterior Angles Theorem: Hence, d = | ax + by + c| /\(\sqrt{a + b}\) 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). Hence, (2, 4); m = \(\frac{1}{2}\) We want to prove L1 and L2 are parallel and we will prove this by using Proof of Contradiction The lines skew to \(\overline{Q R}\) are: \(\overline{J N}\), \(\overline{J K}\), \(\overline{K L}\), and \(\overline{L M}\), Question 4. : n; same-side int. c = -1 1 1 = 2 = 3 = 4 = 5 = 6 = 7 = 53.7, Work with a partner. Given: 1 and 3 are supplementary Hence, from the above, X (3, 3), Y (2, -1.5) Therefore, they are parallel lines. We can observe that the given pairs of angles are consecutive interior angles ATTENDING TO PRECISION For example, the letter H, in which the vertical lines are parallel and the horizontal line is perpendicular to both the vertical lines. Substitute (1, -2) in the above equation (7x 11) = (4x + 58) 3.4). The product of the slopes of the perpendicular lines is equal to -1 Justify your answer. The following table shows the difference between parallel and perpendicular lines. Now, VOCABULARY The parallel lines are the lines that do not have any intersection point Proof: Question 17. 8 = 65. The given figure shows that angles 1 and 2 are Consecutive Interior angles y = -x We know that, Find an equation of line q. 1 and 8 (11x + 33) and (6x 6) are the interior angles Any fraction that contains 0 in the denominator has its value undefined c. y = 5x + 6 Question 3. So, Slope of ST = \(\frac{2}{-4}\) XY = \(\sqrt{(3 + 3) + (3 1)}\) She says one is higher than the other. The give pair of lines are: Compare the given points with Two nonvertical lines in the same plane, with slopes \(m_{1}\) and \(m_{2}\), are perpendicular if the product of their slopes is \(1: m1m2=1\). P = (4 + (4 / 5) 7, 1 + (4 / 5) 1) Look at the diagram in Example 1. Hence, from the above, Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. We get, Parallel Curves Homework 2 - State whether the given pair are parallel, perpendicular, or intersecting. We know that, The given figure is: A triangle has vertices L(0, 6), M(5, 8). y = \(\frac{1}{5}\)x + c The coordinates of P are (3.9, 7.6), Question 3. The point of intersection = (\(\frac{4}{5}\), \(\frac{13}{5}\)) Substitute (3, 4) in the above equation We know that, Hence, from the above, 1 = 76, 2 = 104, 3 = 76, and 4 = 104, Work with a partner: Use dynamic geometry software to draw two parallel lines. x = 6, Question 8. For example, if the equations of two lines are given as: y = 1/4x + 3 and y = - 4x + 2, we can see that the slope of one line is the negative reciprocal of the other. The given point is: (-1, 5) 140 21 32 = 6x d = \(\sqrt{(300 200) + (500 150)}\) 2: identify a parallel or perpendicular equation to a given graph or equation. We get ERROR ANALYSIS Begin your preparation right away and clear the exams with utmost confidence. If the corresponding angles are congruent, then the two lines that cut by a transversal are parallel lines Two lines that do not intersect and are also not parallel are ________ lines. We know that, It is given that a coordinate plane has been superimposed on a diagram of the football field where 1 unit is 20 feet. Decide whether there is enough information to prove that m || n. If so, state the theorem you would use. Now, If two lines are intersected by a third line, is the third line necessarily a transversal? From the given figure, So, So, So, Justify your answer with a diagram. We can conclude that the distance that the two of the friends walk together is: 255 yards. We can observe that y = -2x + 1 The given point is:A (6, -1) If twolinesintersect to form a linear pair of congruent angles, then thelinesareperpendicular. The line that passes through point F that appear skew to \(\overline{E H}\) is: \(\overline{F C}\), Question 2. We know that, 2x y = 4 y = x \(\frac{28}{5}\) So, Given that, Pot of line and points on the lines are given, we have to as shown. By using the Corresponding angles Theorem, Using X and Y as centers and an appropriate radius, draw arcs that intersect. We can observe that the pair of angle when \(\overline{A D}\) and \(\overline{B C}\) are parallel is: APB and DPB, b. So, Answer: ABSTRACT REASONING Hence, from the above, A(- 2, 3), y = \(\frac{1}{2}\)x + 1 If two straight lines lie in the same plane, and if they never intersect each other, they are called parallel lines. x = 14.5 We can conclude that 1 2. Hence, from the above, The given equation is: Answer: Question 24. Click here for a Detailed Description of all the Parallel and Perpendicular Lines Worksheets. a.) So, y = 3x + 9 -(1) Answer: 4 and 5 x = 35 and y = 145, Question 6. m1 and m3 a. = (\(\frac{-2}{2}\), \(\frac{-2}{2}\)) COMPLETE THE SENTENCE 2 = 180 3 Is quadrilateral QRST a parallelogram? Answer: From the given figure, So, We know that, Question 1. We can observe that 3 and 8 are consecutive exterior angles. The given pair of lines are: Answer: The slope of line a (m) = \(\frac{y2 y1}{x2 x1}\) 8 6 = b -x x = -3 4 The slope of line l is greater than 0 and less than 1. y = mx + c From the given figure, d = 364.5 yards Parallel and perpendicular lines have one common characteristic between them. such as , are perpendicular to the plane containing the floor of the treehouse. The lines perpendicular to \(\overline{E F}\) are: \(\overline{F B}\) and \(\overline{F G}\), Question 3. So, We can conclude that Hence, from the above, The lines that do not intersect to each other and are coplanar are called Parallel lines So, The slopes are equal fot the parallel lines State which theorem(s) you used. w y and z x When the corresponding angles are congruent, the two parallel lines are cut by a transversal MODELING WITH MATHEMATICS Proof: Hence, from the above, Write an equation of the line passing through the given point that is parallel to the given line. We know that, We can say that . Prove the Relationship: Points and Slopes This section consists of exercises related to slope of the line. What is m1? Identifying Parallel Lines Worksheets m is the slope No, your friend is not correct, Explanation: Answer: Question 24. Explain your reasoning. Hence, from the above, Hence, from the above, So, Explain. Is b || a? We can conclude that both converses are the same Hence, from the above, y = x 6 -(1) Hence, These Parallel and Perpendicular Lines Worksheets will give the slopes of two lines and ask the student if the lines are parallel, perpendicular, or neither. 5 = 8 Slope of JK = \(\frac{n 0}{0 0}\) The equation that is perpendicular to the given line equation is: The Converse of the Corresponding Angles Theorem says that if twolinesand a transversal formcongruentcorresponding angles, then thelinesare parallel. Alternate Exterior angle Theorem: Slope of ST = \(\frac{1}{2}\), Slope of TQ = \(\frac{3 6}{1 2}\) a is both perpendicular to b and c and b is parallel to c, Question 20. c.) Parallel lines intersect each other at 90. The slope is: \(\frac{1}{6}\) By comparing the given equation with Question 31. The lines that are a straight angle with the given line and are coplanar is called Perpendicular lines So, So, a. The postulates and theorems in this book represent Euclidean geometry. 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 2x = 7 We know that, A(0, 3), y = \(\frac{1}{2}\)x 6 The given line has the slope \(m=\frac{1}{7}\), and so \(m_{}=\frac{1}{7}\). We can observe that the product of the slopes are -1 and the y-intercepts are different The points are: (3, 4), (\(\frac{3}{2}\), \(\frac{3}{2}\)) All its angles are right angles. (- 3, 7) and (8, 6) So, Answer: ax + by + c = 0 Alternate Interior Angles are a pair of angleson the inner side of each of those two lines but on opposite sides of the transversal. 6 (2y) 6(3) = 180 42 The equation that is parallel to the given equation is: FCJ and __________ are alternate interior angles. Perpendicular lines have slopes that are opposite reciprocals. Answer: y = -x + c = (\(\frac{8 + 0}{2}\), \(\frac{-7 + 1}{2}\)) 1 = 180 57 The parallel lines have the same slopes ERROR ANALYSIS We were asked to find the equation of a line parallel to another line passing through a certain point. = \(\frac{8}{8}\) Find the distance from the point (- 1, 6) to the line y = 2x. Now, The equation of the line that is parallel to the line that represents the train tracks is: 69 + 111 = 180 MAKING AN ARGUMENT THINK AND DISCUSS, PAGE 148 1. (C) are perpendicular Answer: x = \(\frac{153}{17}\) Question 4. From the given figure, Slope of AB = \(\frac{4}{6}\) Explain your reasoning. We can solve for \(m_{1}\) and obtain \(m_{1}=\frac{1}{m_{2}}\). We can observe that 4 = 105, To find 5: We can conclude that the distance from point A to the given line is: 5.70, Question 5. Each unit in the coordinate plane corresponds to 10 feet Question 8. 6 + 4 = 180, Question 9. Hence, Is it possible for all eight angles formed to have the same measure? ax + by + c = 0 5y = 3x 6 We know that, m2 = \(\frac{1}{2}\) 1 = 2 AC is not parallel to DF. m = \(\frac{3}{-1.5}\) So, Answer: There are many shapes around us that have parallel and perpendicular lines in them. Answer: Slope (m) = \(\frac{y2 y1}{x2 x1}\) Compare the given points with (x1, y1), (x2, y2) Identify all the pairs of vertical angles. c = -2 Slope (m) = \(\frac{y2 y1}{x2 x1}\) then they are congruent. We know that, Given 1 3 Hence, from the above, = 3, The slope of line d (m) = \(\frac{y2 y1}{x2 x1}\) Answer: c = -5 y = \(\frac{1}{5}\)x + \(\frac{4}{5}\) Now, Answer: Answer: Answer: Question 38. The equation that is perpendicular to the given equation is: Which point should you jump to in order to jump the shortest distance? 61 and y are the alternate interior angles We can conclude that \(m_{}=10\) and \(m_{}=\frac{1}{10}\), Exercise \(\PageIndex{4}\) Parallel and Perpendicular Lines. Answer: The given point is: A (2, -1) The given figure is: The given figure is: y = \(\frac{1}{3}\)x + \(\frac{16}{3}\), Question 5. b = 19 -1 = \(\frac{-2}{7 k}\) The distance from the point (x, y) to the line ax + by + c = 0 is: y = mx + b d = | 2x + y | / \(\sqrt{2 + (1)}\) We can conclude that We know that, Hence, from the above, In the diagram below. The slopes of the parallel lines are the same So, Explain your reasoning. y = \(\frac{1}{6}\)x 8 Compare the given equation with m = \(\frac{3 0}{0 + 1.5}\) Now, Answer: In Exercise 31 on page 161, from the coordinate plane, Perpendicular lines do not have the same slope. y = \(\frac{2}{3}\) CRITICAL THINKING m2 = \(\frac{1}{2}\), b2 = 1 Use the results of Exploration 1 to write conjectures about the following pairs of angles formed by two parallel lines and a transversal. c = -3 d = 17.02 From the given figure, Hence, from the above, Parallel and Perpendicular Lines Maintaining Mathematical Proficiency Page 123, Parallel and Perpendicular Lines Mathematical Practices Page 124, 3.1 Pairs of Lines and Angles Page(125-130), Lesson 3.1 Pairs of Lines and Angles Page(126-128), Exercise 3.1 Pairs of Lines and Angles Page(129-130), 3.2 Parallel Lines and Transversals Page(131-136), Lesson 3.2 Parallel Lines and Transversals Page(132-134), Exercise 3.2 Parallel Lines and Transversals Page(135-136), 3.3 Proofs with Parallel Lines Page(137-144), Lesson 3.3 Proofs with Parallel Lines Page(138-141), Exercise 3.3 Proofs with Parallel Lines Page(142-144), 3.1 3.3 Study Skills: Analyzing Your Errors Page 145, 3.4 Proofs with Perpendicular Lines Page(147-154), Lesson 3.4 Proofs with Perpendicular Lines Page(148-151), Exercise 3.4 Proofs with Perpendicular Lines Page(152-154), 3.5 Equations of Parallel and Perpendicular Lines Page(155-162), Lesson 3.5 Equations of Parallel and Perpendicular Lines Page(156-159), Exercise 3.5 Equations of Parallel and Perpendicular Lines Page(160-162), 3.4 3.5 Performance Task: Navajo Rugs Page 163, Parallel and Perpendicular Lines Chapter Review Page(164-166), Parallel and Perpendicular Lines Test Page 167, Parallel and Perpendicular Lines Cumulative Assessment Page(168-169), Big Ideas Math Answers Grade 2 Chapter 15 Identify and Partition Shapes, Big Ideas Math Answers Grade 6 Chapter 1 Numerical Expressions and Factors, enVision Math Common Core Grade 7 Answer Key | enVision Math Common Core 7th Grade Answers, Envision Math Common Core Grade 5 Answer Key | Envision Math Common Core 5th Grade Answers, Envision Math Common Core Grade 4 Answer Key | Envision Math Common Core 4th Grade Answers, Envision Math Common Core Grade 3 Answer Key | Envision Math Common Core 3rd Grade Answers, enVision Math Common Core Grade 2 Answer Key | enVision Math Common Core 2nd Grade Answers, enVision Math Common Core Grade 1 Answer Key | enVision Math Common Core 1st Grade Answers, enVision Math Common Core Grade 8 Answer Key | enVision Math Common Core 8th Grade Answers, enVision Math Common Core Kindergarten Answer Key | enVision Math Common Core Grade K Answers, enVision Math Answer Key for Class 8, 7, 6, 5, 4, 3, 2, 1, and K | enVisionmath 2.0 Common Core Grades K-8, enVision Math Common Core Grade 6 Answer Key | enVision Math Common Core 6th Grade Answers, Go Math Grade 8 Answer Key PDF | Chapterwise Grade 8 HMH Go Math Solution Key. Now, We can conclude that the given statement is not correct. c = 4 3 y 3y = -17 7 In Exercises 27-30. find the midpoint of \(\overline{P Q}\). Explain your reasoning. Explain your reasoning. = \(\frac{1}{3}\) x = 12 and y = 7, Question 3. We can observe that the given lines are perpendicular lines 1 = 180 138 Then, by the Transitive Property of Congruence, The representation of the given pair of lines in the coordinate plane is: We can observe that (4.3.1) - Parallel and Perpendicular Lines Parallel lines have the same slope and different y- intercepts. From the given figure, x y = 4 consecutive interior The point of intersection = (0, -2) THOUGHT-PROVOKING The given figure is: Question 13. Use the numbers and symbols to create the equation of a line in slope-intercept form Imagine that the left side of each bar extends infinitely as a line. The equation that is perpendicular to the given line equation is: (x + 14)= 147 Answer: 42 = (8x + 2) Now, Use a graphing calculator to graph the pair of lines. 1 = 2 From the given figure, To find the value of b, Compare the given equation with For a vertical line, The equation of the line along with y-intercept is: y = -2x + 3 Converse: The coordinates of the subway are: (500, 300) EG = \(\sqrt{(x2 x1) + (y2 y1)}\) m is the slope We know that, The lines that do not intersect and are not parallel and are not coplanar are Skew lines The coordinates of line 1 are: (10, 5), (-8, 9) PROOF (2) The angles that have the common side are called Adjacent angles The given lines are perpendicular lines d = | ax + by + c| /\(\sqrt{a + b}\) a.) y = -x + c Now, So, Parallel to \(y=\frac{1}{2}x+2\) and passing through \((6, 1)\). We know that, The given point is: P (-8, 0) y = \(\frac{1}{5}\) (x + 4) According to the Transitive Property of parallel lines, Now, So, a. Embedded mathematical practices, exercises provided make it easy for you to understand the concepts quite quickly. Geometry chapter 3 parallel and perpendicular lines answer key Apps can be a great way to help learners with their math. The given equation is: P = (22.4, 1.8) Answer: 3x 5y = 6 So, y = \(\frac{1}{2}\)x + 2 ANALYZING RELATIONSHIPS y = \(\frac{1}{2}\)x 6 y = \(\frac{3}{2}\)x + 2 b. From the given figure, y = \(\frac{1}{2}\)x + c We know that, The equation of the line that is parallel to the given line equation is: The rope is pulled taut. The coordinates of a quadrilateral are: \(\frac{5}{2}\)x = \(\frac{5}{2}\) Hence, from the above, c. m5=m1 // (1), (2), transitive property of equality a. Hence, from the above, We can observe that We can conclude that the given pair of lines are perpendicular lines, Question 2. Hence, A _________ line segment AB is a segment that represents moving from point A to point B. Determine whether the converse is true. Algebra 1 worksheet 36 parallel and perpendicular lines answer key. So, The given point is: A (-1, 5) Question 37. The coordinates of line d are: (0, 6), and (-2, 0) Hence, from the above, MAKING AN ARGUMENT Parallel lines do not intersect each other So, We know that, Perpendicular to \(4x5y=1\) and passing through \((1, 1)\). In the proof in Example 4, if you use the third statement before the second statement. How do you know that the lines x = 4 and y = 2 are perpendiculars? Answer: Simply click on the below available and learn the respective topics in no time. Substitute A (-1, 5) in the above equation 2x = -6 Substitute A (8, 2) in the above equation Answer: Question 32. m = = So, slope of the given line is Question 2. From the given figure, y = 132 Compare the given equation with We have to find the point of intersection then the slope of a perpendicular line is the opposite reciprocal: The mathematical notation \(m_{}\) reads \(m\) perpendicular. We can verify that two slopes produce perpendicular lines if their product is \(1\). This contradicts what was given,that angles 1 and 2 are congruent. Hence, from the above figure, The given equation is: According to Euclidean geometry, 1 8, d. m6 + m ________ = 180 by the Consecutive Interior Angles Theorem (Thm. Compare the given equation with d = | x y + 4 | / \(\sqrt{1 + (-1)}\) From the given figure, Now, Hence, from the above, A(3, 4),y = x + 8 Hence, from the above, The given equation is: So, by the Corresponding Angles Converse, g || h. Question 5. Use the Distance Formula to find the distance between the two points. = 0 The letter A has a set of perpendicular lines. Although parallel and perpendicular lines are the two basic and most commonly used lines in geometry, they are quite different from each other. = 3 Possible answer: plane FJH plane BCD 2a. y = 180 48 We can conclude that Hence, from the above figure, = 2 Perpendicular to \(\frac{1}{2}x\frac{1}{3}y=1\) and passing through \((10, 3)\). If the slope of AB and CD are the same value, then they are parallel. Answer: Answer: The given point is: (6, 1) Question 3. 3: write the equation of a line through a given coordinate point . Determine the slope of a line perpendicular to \(3x7y=21\). Substitute (4, -3) in the above equation The given equation is: We can conclude that the line that is parallel to the given line equation is: The consecutive interior angles are: 2 and 5; 3 and 8. We can observe that Possible answer: 2 and 7 c. Possible answer: 1 and 8 d. Possible answer: 2 and 3 3. 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 points are: (-3, 7), (0, -2) Hence, Answer: Legal. Answer: We know that, c = 3 4 It is given that 4 5. The missing information the student assuming from the diagram is: The equation of the parallel line that passes through (1, 5) is: Slope of AB = \(\frac{2}{3}\) Find the distance front point A to the given line. The given point is: P (3, 8) Hence, Answer: y = mx + c Slope of TQ = \(\frac{-3}{-1}\) y = \(\frac{137}{5}\) m2 = \(\frac{1}{2}\) d = \(\sqrt{(x2 x1) + (y2 y1)}\) The equation of a line is: From the figure, 3x 2x = 20 We know that, MAKING AN ARGUMENT Prove \(\overline{A B} \| \overline{C D}\) Here is a quick review of the point/slope form of a line. From the given figure, (2) y = \(\frac{1}{2}\)x + 7 -(1) So, y = \(\frac{1}{2}\)x + 2 We can conclude that Now, So, (1) = Eq. If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent