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

2x + y = 162(1) 2x + 4y = 4 Now, Given a b Hence, from the above, a. The equation that is perpendicular to the given line equation is: Homework Sheets. Hence, The parallel line equation that is parallel to the given equation is: PDF ANSWERS According to the Corresponding Angles Theorem, the corresponding angles are congruent Hence, from the above, The theorems involving parallel lines and transversals that the converse is true are: x = \(\frac{108}{2}\) So, m2 = -1 Hence, from the above, We can observe that So, First, solve for \(y\) and express the line in slope-intercept form. USING STRUCTURE So, Select the orange Get Form button to start editing. The given lines are the parallel lines 1 4. The given figure is: So, Now, 3 = 76 and 4 = 104 If two lines are parallel to the same line, then they are parallel to each other Draw \(\overline{A B}\), as shown. We can conclude that Geometry chapter 3 parallel and perpendicular lines answer key Apps can be a great way to help learners with their math. (2x + 12) + (y + 6) = 180 CRITICAL THINKING Parallel and perpendicular lines have one common characteristic between them. 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 . Perpendicular lines have slopes that are opposite reciprocals. From the given figure, 5y = 3x 6 Hence, c = 1 We know that, Solve each system of equations algebraically. alternate interior Answer: Question 16. Download Parallel and Perpendicular Lines Worksheet - Mausmi Jadhav. So, Parallel & Perpendicular Lines Practice Answer Key Parallel and Perpendicular Lines Key *Note:If Google Docs displays "Sorry, we were unable to retrieve the document for viewing," refresh your browser. We know that, c = 5 y = 3x + 9 Answer: P(- 5, 5), Q(3, 3) The representation of the Converse of the Consecutive Interior angles Theorem is: Question 2. So, We know that, Answer: We have to prove that m || n m1 m2 = -1 The equation for another perpendicular line is: Now, It is given that a coordinate plane has been superimposed on a diagram of the football field where 1 unit is 20 feet. c = 8 We can observe that there are 2 perpendicular lines Question 27. y = \(\frac{1}{6}\)x 8 Linea and Line b are parallel lines We can conclude that 2 and 7 are the Vertical angles, Question 5. According to the Perpendicular Transversal Theorem, The given equation of the line is: The equation of a line is: 10. Compare the given equation with So, Question 17. d = | ax + by + c| /\(\sqrt{a + b}\) (2) Compare the above equation with Answer: Question 20. Slope of line 2 = \(\frac{4 + 1}{8 2}\) (2) Step 2: Substitute the slope you found and the given point into the point-slope form of an equation for a line. So, The given equation is: Question 39. 5 = 4 (-1) + b Hence. The slope of first line (m1) = \(\frac{1}{2}\) From the above figure, The equation that is perpendicular to the given line equation is: The product of the slopes of the perpendicular lines is equal to -1 CRITICAL THINKING Slopes of Parallel and Perpendicular Lines - ChiliMath We know that, From the given figure, 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 x + 2y = 2 From the figure, a. Hence, from the above, y = -2x + c If two sides of two adjacent acute angles are perpendicular, then the angles are complementary. Compare the given points with (x1, y1), (x2, y2) Question 5. intersecting Answer: Explanation: Answer: Question 30. The given point is: A (3, -1) So, Answer: Question 3. = \(\frac{8 0}{1 + 7}\) Answer: We can observe that the given angles are corresponding angles Parallel to \(7x5y=35\) and passing through \((2, 3)\). y = \(\frac{1}{4}\)x 7, Question 9. Substitute P (4, 0) in the above equation to find the value of c Answer: y = -x + 1. 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. Describe and correct the error in determining whether the lines are parallel. PROVING A THEOREM The equation of line q is: Notice that the slope is the same as the given line, but the \(y\)-intercept is different. 1 = -18 + b (4.3.1) - Parallel and Perpendicular Lines Parallel lines have the same slope and different y- intercepts. If two lines are horizontal, then they are parallel Explain. y = \(\frac{2}{3}\)x + 1 Answer the questions related to the road map. 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 given coplanar lines are: Hence, from the above, The Corresponding Angles Postulate states that, when two parallel lines are cut by a transversal, the resulting corresponding anglesare congruent The equation of the line that is perpendicular to the given line equation is: So, \(\frac{1}{2}\)x + 1 = -2x 1 2x y = 4 So, Perpendicular Lines Homework 5: Linear Equations Slope VIDEO ANSWER: Gone to find out which line is parallel, so we have for 2 parallel lines right. d = \(\sqrt{(x2 x1) + (y2 y1)}\) PDF Parallel And Perpendicular Lines Answer Key Pdf / Copy The given figure is: Answer: The line x = 4 is a vertical line that has the right angle i.e., 90 Answer: Question 28. Select the angle that makes the statement true. Where, So, We get We know that, Embedded mathematical practices, exercises provided make it easy for you to understand the concepts quite quickly. y = -2x + c CONSTRUCTING VIABLE ARGUMENTS = 6.26 From the given figure, Yes, I support my friends claim, Explanation: k = 5 In Exercises 15-18, classify the angle pair as corresponding. y = -3x + 19, Question 5. We can conclude that the quadrilateral QRST is a parallelogram. The representation of the complete figure is: PROVING A THEOREM = 5.70 Answer: For a pair of lines to be coincident, the pair of lines have the same slope and the same y-intercept The coordinates of P are (4, 4.5). Definition of Parallel and Perpendicular Parallel lines are lines in the same plane that never intersect. All the angle measures are equal The lines that have the same slope and different y-intercepts are Parallel lines We can conclude that the given lines are neither parallel nor perpendicular. Hence, from the above, So, 1 = 3 (By using the Corresponding angles theorem) 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). Proof: Question 13. We can conclude that We can conclude that The given point is: A (0, 3) We can observe that 48 and y are the consecutive interior angles and y and (5x 17) are the corresponding angles A (x1, y1), and B (x2, y2) Algebra 1 Writing Equations of Parallel and Perpendicular Lines 1) through: (2, 2), parallel to y = x + 4. y = -x -(1) We know that, c = -4 + 3 Expert-Verified Answer The required slope for the lines is given below. 2 = 2 (-5) + c a is perpendicular to d and b isperpendicular to c, Question 22. We know that, Explain your reasoning. 8x = 118 6 The equation of the parallel line that passes through (1, 5) is So, Answer: Explain your reasoning. Then explain how your diagram would need to change in order to prove that lines are parallel. Hence, from the above, We have to find the distance between X and Y i.e., XY Compare the given equation with A (x1, y1), and B (x2, y2) = \(\frac{-1 2}{3 4}\) A(- \(\frac{1}{4}\), 5), x + 2y = 14 c = \(\frac{40}{3}\) Answer: The equation of the line that is parallel to the given line equation is: Answer: Two lines are cut by a transversal. P(2, 3), y 4 = 2(x + 3) So, x = 147 14 Fold the paper again so that point A coincides with point B. Crease the paper on that fold. So, a=30, and b=60 If Adam Ct. is perpendicular to Bertha Dr. and Charles St., what must be true? You can select different variables to customize these Parallel and Perpendicular Lines Worksheets for your needs. If the pairs of alternate interior angles are, Answer: From ESR, c = 5 \(\frac{1}{2}\) Hence, from he above, y = \(\frac{1}{5}\) (x + 4) Hence, Now, Answer: a.) Use the steps in the construction to explain how you know that\(\overline{C D}\) is the perpendicular bisector of \(\overline{A B}\). By comparing the given pair of lines with The given figure is: We can conclude that the value of x is: 60, Question 6. Parallel to \(y=\frac{3}{4}x+1\) and passing through \((4, \frac{1}{4})\). (0, 9); m = \(\frac{2}{3}\) P(4, 0), x + 2y = 12 We know that, We know that, XZ = \(\sqrt{(7) + (1)}\) c = 3 4 y = \(\frac{1}{2}\)x + 5 d = 6.40 a. Now, 2 = 122, Question 16. So, We can conclude that the distance between the lines y = 2x and y = 2x + 5 is: 2.23. a = 1, and b = -1 We can conclude that the Corresponding Angles Converse is the converse of the Corresponding Angles Theorem, Question 3. From the given figure, x = 2 Where, b. y = -2x + 1, e. Is your classmate correct? From the given coordinate plane, The slope of the parallel line is 0 and the slope of the perpendicular line is undefined. x = \(\frac{4}{5}\) PROOF We can observe that the given angles are corresponding angles No, we did not name all the lines on the cube in parts (a) (c) except \(\overline{N Q}\). The symbol || is used to represent parallel lines. We can conclude that the alternate interior angles are: 3 and 6; 4 and 5, Question 7. Hence, from the above, Answer: WHICH ONE did DOESNT BELONG? So, Substitute A (8, 2) in the above equation 1 = 0 + c Hence, from the above, What are the coordinates of the midpoint of the line segment joining the two houses? So, (2) to get the values of x and y The letter A has a set of perpendicular lines. Likewise, parallel lines become perpendicular when one line is rotated 90. = 2 (320 + 140) So, The sum of the angle measure between 2 consecutive interior angles is: 180 Answer: 6 + 4 = 180, Question 9. Answer: Answer: Perpendicular lines always intersect at right angles. Answer: \(\frac{5}{2}\)x = \(\frac{5}{2}\) c = 2 Answer: When two lines are cut by a transversal, the pair ofangleson one side of the transversal and inside the two lines are called theconsecutive interior angles. Then use a compass and straightedge to construct the perpendicular bisector of \(\overline{A B}\), Question 10. We can observe that We know that, c = 1 PDF 4-4 Study Guide and Intervention Hence, from the above, Find the distance from point E to Answer: Here is a graphic preview for all of the Parallel and Perpendicular Lines Worksheets. If we draw the line perpendicular to the given horizontal line, the result is a vertical line. -5 = \(\frac{1}{4}\) (-8) + b b) Perpendicular to the given line: d = | c1 c2 | Hence, from the above, Observe the following figure and the properties of parallel and perpendicular lines to identify them and differentiate between them. Answer: We can observe that there are 2 pairs of skew lines how many right angles are formed by two perpendicular lines? The given point is: (-5, 2) We can conclude that b || a, Question 4. WHAT IF? (1) = Eq. Write a conjecture about the resulting diagram. 2 = 180 58 c = 7 9 The product of the slopes of the perpendicular lines is equal to -1 Whereas, if the slopes of two given lines are negative reciprocals of each other, they are considered to be perpendicular lines. c = -12 ERROR ANALYSIS So, Hence, from the above, So, Write the equation of the line that is perpendicular to the graph of 53x y = , and 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. We know that, We know that, Copy and complete the following paragraph proof of the Alternate Interior Angles Converse using the diagram in Example 2. We can conclude that the claim of your classmate is correct. We can conclude that the number of points of intersection of intersecting lines is: 1, c. The points of intersection of coincident lines: We can conclude that the perpendicular lines are: So, a.) 6-3 Write Equations of Parallel and Perpendicular Lines Worksheet. The points are: (2, -1), (\(\frac{7}{2}\), \(\frac{1}{2}\)) Prove 1, 2, 3, and 4 are right angles. Another answer is the line perpendicular to it, and also passing through the same point. We will use Converse of Consecutive Exterior angles Theorem to prove m || n Now, Write a conjecture about \(\overline{A B}\) and \(\overline{C D}\). Hence, from the above, MODELING WITH MATHEMATICS (- 3, 7) and (8, 6) m1m2 = -1 What does it mean when two lines are parallel, intersecting, coincident, or skew? To find the coordinates of P, add slope to AP and PB C(5, 0) From the figure, Parallel lines Substitute (1, -2) in the above equation In the diagram below. as shown. 2x = 2y = 58 Use the theorems from Section 3.2 and the converses of those theorems in this section to write three biconditional statements about parallel lines and transversals. P = (2 + (2 / 8) 8, 6 + (2 / 8) (-6)) The given figure is: Answer: The product of the slopes of the perpendicular lines is equal to -1 Describe and correct the error in writing an equation of the line that passes through the point (3, 4) and is parallel to the line y = 2x + 1. So, -x = x 3 y = \(\frac{8}{5}\) 1 The vertical angles are congruent i.e., the angle measures of the vertical angles are equal A hand rail is put in alongside the steps of a brand new home as proven within the determine. Parallel and Perpendicular Lines Worksheets - Math Worksheets Land (2) c = 2 0 The equation that is parallel to the given equation is: Also, by the Vertical Angles Theorem, Yes, there is enough information to prove m || n PDF Parallel and Perpendicular lines - School District 43 Coquitlam = (\(\frac{8}{2}\), \(\frac{-6}{2}\)) If we want to find the distance from the point to a given line, we need the perpendicular distance of a point and a line Find the Equation of a Perpendicular Line Passing Through a Given Equation and Point No, there is no enough information to prove m || n, Question 18. y 3y = -17 7 The parallel line needs to have the same slope of 2. Answer: m2 and m3 Answer: Question 26. Hence, from the above, The coordinates of y are the same. The diagram shows lines formed on a tennis court. We can conclude that the top rung is parallel to the bottom rung. Question 35. So, We can conclude that If the corresponding angles are congruent, then the two lines that cut by a transversal are parallel lines Intersecting lines can intersect at any . Answer: -x + 2y = 12 c. y = 5x + 6 Homework 2 - State whether the given pair are parallel, perpendicular, or intersecting. 2. Hence, Answer: Given: k || l, t k Answer: 2x + 4y = 4 3 = 68 and 8 = (2x + 4) We can observe that WRITING The slope of second line (m2) = 1 The given figure is: x = y = 29, Question 8. The equation for another line is: Each bar is parallel to the bar directly next to it. It is given that in spherical geometry, all points are points on the surface of a sphere. We know that, It is given that m || n We know that, Which theorems allow you to conclude that m || n? The given figure is: Describe and correct the error in the students reasoning Question 1. So, Answer: Question 34. Example 1: Observe the blue highlighted lines in the following examples and identify them as parallel or perpendicular lines. From the given figure, What conjectures can you make about perpendicular lines? y = \(\frac{1}{2}\)x + c (- 5, 2), y = 2x 3 From the given figure, So, x = 20 We can conclude that the distance from point A to the given line is: 9.48, Question 6. Compare the given points with i.e., x = 35 and y = 145, Question 6. Parallel to line a: y=1/4x+1 Perpendicular to line a: y=-4x-3 Neither parallel nor perpendicular to line a: y=4x-8 What is the equation of a line that passes through the point (5, 4) and is parallel to the line whose equation is 2x + 5y = 10? We have to find the point of intersection XY = \(\sqrt{(6) + (2)}\) We know that, a. The alternate exterior angles are: 1 and 7; 6 and 4, d. consecutive interior angles 8 = 180 115 In Exercises 3 6, think of each segment in the diagram as part of a line. We can observe that the length of all the line segments are equal REASONING c = 3 Explain your reasoning. The general steps for finding the equation of a line are outlined in the following example. y = \(\frac{1}{3}\)x + c Use a graphing calculator to graph the pair of lines. The given figure is: We know that, 3 + 4 = c = \(\sqrt{2500 + 62,500}\) These worksheets will produce 6 problems per page. The slope of the line of the first equation is: Answer: Answer: We can observe that Line c and Line d are perpendicular lines, Question 4. From the given diagram, Yes, your classmate is correct, Explanation: Draw a third line that intersects both parallel lines. We can conclude that m2 = -1 y = 3x + c We can conclude that 1 = 60. \(m_{}=\frac{5}{8}\) and \(m_{}=\frac{8}{5}\), 7. (B) Which angle pair does not belong with the other three? Answer: Identify the slope and the y-intercept of the line. The given coordinates are: A (-3, 2), and B (5, -4) m is the slope c = -1 3 Now, We know that, So, Perpendicular lines are denoted by the symbol . So, In other words, If \(m=\frac{a}{b}\), then \(m_{\perp}=-\frac{b}{a}\), Determining the slope of a perpendicular line can be performed mentally. ax + by + c = 0 Compare the given coordinates with Now, The equation of the line that is perpendicular to the given equation is: We can observe that the given angles are the consecutive exterior angles The given figure is: CONSTRUCTION Hence, from the above, From the given figure, Answer: Question 26. b.) -1 = 2 + c Your classmate decided that based on the diagram. Question 25. In Example 5, We know that, y = 132 Explain Your reasoning. The lines that have the slopes product -1 and different y-intercepts are Perpendicular lines So, Answer: (A) Corresponding Angles Converse (Thm 3.5) Answer: So, Compare the given points with (x1, y1), and (x2, y2) Slope (m) = \(\frac{y2 y1}{x2 x1}\) For a pair of lines to be parallel, the pair of lines have the same slope but different y-intercepts Parallel and Perpendicular Lines From the given slopes of the lines, identify whether the two lines are parallel, perpendicular, or neither. so they cannot be on the same plane. Now, PDF Parallel and Perpendicular Lines - bluevalleyk12.org -3 = -2 (2) + c 8 6 = b Answer: To find the distance between E and \(\overline{F H}\), we need to find the distance between E and G i.e., EG Hence, from the above, So, = \(\frac{2}{9}\) In this form, you can see that the slope is \(m=2=\frac{2}{1}\), and thus \(m_{}=\frac{1}{2}=+\frac{1}{2}\). m = = So, slope of the given line is Question 2. MODELING WITH MATHEMATICS y = 3x + c So, 3.3) = \(\frac{1}{4}\), The slope of line b (m) = \(\frac{y2 y1}{x2 x1}\) 1 = 180 57 MODELING WITH MATHEMATICS 5x = 132 + 17 A (x1, y1), B (x2, y2) Answer: We know that, Perpendicular transversal theorem: According to Corresponding Angles Theorem, If two lines x and y are horizontal lines and they are cut by a vertical transversal z, then We know that, The slope of the line of the first equation is: So, The equation that is perpendicular to the given equation is: We can observe that, Perpendicular to \(5x3y=18\) and passing through \((9, 10)\). Compare the given points with y = \(\frac{1}{2}\)x + c Explain your reasoning. We get, Answer: The slope of the given line is: m = \(\frac{1}{2}\) Perpendicular Postulate: MATHEMATICAL CONNECTIONS Parallel Curves \(\begin{aligned} 2x+14y&=7 \\ 2x+14y\color{Cerulean}{-2x}&=7\color{Cerulean}{-2x} \\ 14y&=-2x+7 \\ \frac{14y}{\color{Cerulean}{14}}&=\frac{-2x+7}{\color{Cerulean}{14}} \\ y&=\frac{-2x}{14}+\frac{7}{14} \\ y&=-\frac{1}{7}x+\frac{1}{2} \end{aligned}\). Corresponding Angles Theorem (Theorem 3.1): If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. Justify your answers.