_{Parallel perpendicular or neither worksheet answers. Course: High school geometry > Unit 6. Lesson 4: Parallel & perpendicular lines on the coordinate plane. Parallel & perpendicular lines intro. Parallel & perpendicular lines from graph. Parallel & perpendicular lines from graph. Classifying quadrilaterals on the coordinate plane. Classifying figures with coordinates. Expert Answer. Ans 41: Step 1: Given line AB with coordinates of A (-1, -4) and that of B (2, 11) Step 2: Given line CD with coordinates of C (1, 1) and that of D (4, 10) Step 3: Let us calculate slopes of both these lines Slope = m = (y2 - y1)/ (x …. Determine whether AB and CD are parallel, perpendicular, or neither. }

_{Parallel and perpendicular line calculator. This calculator find and plot equations of parallel and perpendicular to the given line and passes through given point. The calculator will generate a step-by-step explanation on how to obtain the result. ©0 L2r0 i1F1 A 8K Hu0t ja p HS0o1f htw5aZrdem 6L 4L wCP.P t 1AslZlP tr vijg PhQt hs9 6rMeHsle GrWvPekdB.J R vM ca MdFej Swkibtyh e 2IGnlf bi2nki9tZec 1ADlog pesbKrOab q1n.4-4-Worksheet by Kuta Software LLC Answers to Writing Equations of Parallel and Perpendicular Lines (ID: 1) 1) yWorksheet by Kuta Software LLC Geometry Summer Work - Week #4 Parallel & Perpendicular Slopes & Equations of Lines Name_____ ID: 1 Date_____ ©Q p2o0D1j7S DK[ukttaB USio\fttHweaTrbeD _LWLqCj.h Y WAvlKlD vrhisg[hHt`sG UrmeQsqeIrbvQehdX.-1-Find the slope of each line. 1) x y 2) x y Rewrite in slope-intercept form. Tap for more steps... y = − 4 7x+ 9 7 y = - 4 7 x + 9 7. Using the slope-intercept form, the slope is −4 7 - 4 7. m = −4 7 m = - 4 7. To find an equation that is parallel, the slopes must be equal. Find the parallel line using the point - slope formula. Use the slope −4 7 - 4 7 and a given point (4,−2 ...Shiping up to insure that are grouped by different products represented by her car and parallel perpendicular or neither worksheet answers into flames had discovered last time. Européenne Assurance CurseStudents color the parts of the egg based on whether the lines in the section are parallel, perpendicular, or neither. Coloring fun for bigger kids! Coloring fun for bigger kids! The larger packet contains 5 different worksheets, focusing on identifying types of angles, right triangles, lines, line segments, rays, and types of lines.Line 1: Line 2: Parallel Lines: The lines are parallel if their slopes are equal or the same. That means. Equal Slopes: Graph: Perpendicular Lines: The lines are perpendicular if their slopes are opposite reciprocals of each other. Or, if we multiply their slopes together, we get a product of – \,1 –1 . This means the lines are neither parallel nor perpendicular. So the answer is neither. Now that we have a sense of how the slopes of parallel and perpendicular lines are related, let’s try some more challenging examples which combine the ideas of 6.5 with parallel and perpendicular lines. Example 3:Grade 3 geometry worksheet: Parallel and perpendicular lines Author: K5 Learning Subject: Grade 3 Geometry Worksheet Keywords: Grade 3 geometry worksheet 2D shapes, lines, angles, parallel, area, perimiter Created Date: 5/1/2017 9:55:39 AMCommon misconceptions. Using the y-intercept instead of the coefficient of x (parallel lines); E.g. Take example 1: “The equation of a line A is given as 5y = x − 10.Write the equation of a line that is parallel to A.” After making y the subject so we have the equation y=\frac{1}{5}x−2 the value for the gradient could be incorrectly taken as – 2.Given Slopes of Two Lines Determine if the Lines are Parallel, Perpendicular, or Neither. 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. These worksheets will produce 10 problems per page. We know that if the slopes of the lines are equal then the lines are parallel. If they are negative reciprocals of each other then they are perpendicular. If the slopes are neither then the lines are neither parallel nor perpendicular. We need to put the lines in slope-intercept form y=mx+b in order to determine their slopes. Study with Quizlet and memorize flashcards containing terms like 1. parallel, 1. neither, ... Determine if the following lines are parallel, perpendicular, or neither: y = -7x + 4 y = -7x + 3. 1. perpendicular. 1. Determine if the following lines are parallel, perpendicular, or neither: y = 2/7x - 1 y = -7/2x. About us.Web if you are looking for the parallel perpendicular or neither worksheet answer key, you've come to the right place. Ch 3 parallel and perpendicular lines. Block date topic homework 16 b. Web Download Parallel Perpendicular Or Neither Worksheet All Things Algebra And Get The Answers.Step 6: Parallel and Perpendicular National Curriculum Objectives: Mathematics Year 3: (3G2) Identify horizontal and vertical lines and pairs of perpendicular and parallel lines Differentiation: Developing Questions to support identifying a set of parallel and perpendicular lines, both discretely and within shapes.The line which intersects with one another at \(90°\) are called perpendicular lines. \(2\) or more points that lie on one straight line are called collinear points. Parallel, Perpendicular, and Intersecting Lines – Example 1: State whether the given pair of lines are parallel, perpendicular, or intersecting. Solution: All of the lines shown in the graph are parallel because they have the same slope and different y- intercepts. Lines that are perpendicular intersect to form a \displaystyle {90}^ {\circ } 90∘ -angle. The slope of one line is the negative reciprocal of the other. We can show that two lines are perpendicular if the product of the two slopes is ... To represent a perpendicular, we draw a small square at the corner that forms the right angle. Parallel lines are defined as the two lines drawn at some distance apart. These lines neither intersect nor touch each other. For two lines to be parallel, they are drawn in the same plane. Parallel lines help us understand the relationships between ... Example 2: State true or false using the properties of parallel and perpendicular lines. a.) The letter A has a set of perpendicular lines. b.) The opposite sides of a rectangle are parallel lines. c.) Parallel lines intersect each other at 90°. Solution: Using the properties of parallel and perpendicular lines, we can answer the given ...Worksheet by Kuta Software LLC. -4-. Answers to Writing Equations of Parallel and Perpendicular Lines (ID: 1). 1) y = x. 2) x = 4. 3) y = 3x - 10. 4) y = -. 2.Each side is parallel to its opposite side. Rectangles, squares, and rhombi (more than 1 rhombus) are parallelograms. Lines with the same slope (per the slope formula) — Line 1: m = -3; Line 2: m = -3. Lines with the same rise and run. Look at the picture above. Notice that the slope for each of these lines is -3/2.This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Question: Determine if the two lines with equations and are parallel, perpendicular, or neither. If one line passes through the points and and another line passes through the points and ... F. Parallel & Perpendicular Lines Worksheets (Practice Worksheet, Quiz Worksheet). V. Presentation Outline: A. Introduction. "Understanding the differences and similarities between parallel and perpendicular lines." I. Definitions II. Review of Slopes B. Determine if two lines are parallel or perpendicular. ExampleBe careful! They may be the same line (but with a different equation), and so are not parallel. How do we know if they are really the same line? Check their y-intercepts (where they cross the y-axis) as well as their slope: Example: is y = 3x + 2 parallel to y − 2 = 3x ? For y = 3x + 2: the slope is 3, and y-intercept is 24) neither parallel nor perpendicular 5 The equation of line k is y 1 3 x 2. The equation of line m is 2x 6y 18. Lines k and m are 1) parallel 2) perpendicular 3) the same line 4) neither parallel nor perpendicular 6 The lines represented by the equations 4x 6y 6 and y 2 3 x 1 are 1) parallel 2) the same line 3) perpendicular 4) intersecting ...Parallel Perpendicular or Neither Worksheet Answer Key with Web the codes lead to multiple choice questions where the students have to determine if the equations given are parallel, perpendicular,. Web in this set of printable worksheets for 3rd grade, 4th grade, and 5th grade kids are required to identify whether the pair of.Remember, they must be the opposite reciprocal in order to meet the requirement of perpendicularity. Just like in our previous examples, you can also check by multiplying the slopes. Here you get [latex] + 1[/latex] and not [latex] – 1[/latex], so these lines are not perpendicular either. Therefore, the final answer is “neither“!Web download parallel perpendicular or neither worksheet all things algebra and get the answers. Web parallel lines worksheet and play at each graph below, or perpendicular neither parallel worksheet answer key is there is displayed in to buy and merlot. Enter code log in sign up suggestions for.Parallel lines have the same slope. Perpendicular lines, depending on how you wanna view it, they're kind of the opposite. Let's say this is some line, a line that is perpendicular to that, will not only intersect the line, it won't only intersect the line, it will intersect it at a right angle. At a 90 degree angle.(b) Find the equation of the line that is parallel to L and passes through P. -6-7-8 (c) Find the equation of the line that is perpendicular to L and passes through Q. 21. The line W has equation 3y = 4x – 11. The line V is perpendicular to W and passes through the point (-4, 7). Does V pass through the point (2 3, 7 2)? -11-10-9-5-4-3-2-1 0 ...Parallel Perpendicular or Neither Worksheet Answer Key with Web the codes lead to multiple choice questions where the students have to determine if the equations given are parallel, perpendicular,. Web in this set of printable worksheets for 3rd grade, 4th grade, and 5th grade kids are required to identify whether the pair of.Parallel and Perpendicular Lines. Two lines are said to be parallel if their slopes are the same. This means that the lines are going in exactly the same direction. Two lines are said to be perpendicular if they cross at right angles. Perpendicular lines have slopes that multiply to –1. This means that the slopes are the negative reciprocals ...This parallel, perpendicular, or neither maze contains problems involving:two lines in slope-intercept formtwo lines in standard formtwo points from each line. Students must solve 11 problems to complete the maze. Answer key included! **The answer key shown in the preview is NOT the correct answer key. Sorry students!Two lines with the same y-intercept are perpendicular. 11. Two lines whose slopes are opposites of each other are perpendicular. y5 2 x 15 523 12 y 521 3 x 1 11 parallel perpendicular perpendicular neither never sometimes sometimes y 5 3 4x 2 16 g Write an equation of the line that passes through the given point and is perpendicular to the ...4) neither parallel nor perpendicular 5 The equation of line k is y 1 3 x 2. The equation of line m is 2x 6y 18. Lines k and m are 1) parallel 2) perpendicular 3) the same line 4) neither parallel nor perpendicular 6 The lines represented by the equations 4x 6y 6 and y 2 3 x 1 are 1) parallel 2) the same line 3) perpendicular 4) intersecting ... Parallel and Perpendicular Lines Q 1 : Find the slope of the line passing through the pairs of points and describe the line as rising, falling, horizontal or vertical. a. (2 , 1) , (4 , 5) b. (-1 , 0) , (3 , -5) c. (2 , 1) , (-3 , 1) d. (-1 , 2) , (-1 ,- 5)This graph shows y = 2x − 3. y = 2 x − 3. We want to graph a line parallel to this line and passing through the point (−2, 1) ( − 2, 1). We know that parallel lines have the same slope. So the second line will have the same slope as y = 2x − 3 y = 2 x − 3. That slope is m∥ = 2 m ∥ = 2.Parallel lines have the same slope. Perpendicular lines, depending on how you wanna view it, they're kind of the opposite. Let's say this is some line, a line that is perpendicular to that, will not only intersect the line, it won't only intersect the line, it will intersect it at a right angle. At a 90 degree angle.Parallel and Perpendicular Lines Worksheets What is the Difference Between Parallel and Perpendicular Lines? A line that crosses or intersects another line at 90 degrees is …AP ۱۴۰۰ لړم ۱۲ ... Are the two lines given by y= (-2/3)x + 4 and 3x-2y=2 parallel, perpendicular or neither? ... Quizzes & Worksheets. Classroom Integration. Lesson ...©0 L2r0 i1F1 A 8K Hu0t ja p HS0o1f htw5aZrdem 6L 4L wCP.P t 1AslZlP tr vijg PhQt hs9 6rMeHsle GrWvPekdB.J R vM ca MdFej Swkibtyh e 2IGnlf bi2nki9tZec 1ADlog pesbKrOab q1n.4-4-Worksheet by Kuta Software LLC Answers to Writing Equations of Parallel and Perpendicular Lines (ID: 1) 1) y Note: This worksheet is supported by a flash presentation, under Mausmi’s Math Movies. Mausmi Jadhav Q2: Determine whether the graphs of each pair of equations are parallel, perpendicular or neither. 1. y = 3x + 4 y = 3x + 7 2. y = -4x + 1 4y = x + 3 3. y = 2x - 5 y = 5x - 5 4. y = -1/3x + 2 y = 3x - 5 5. y = 3/5x - 3 5y = 3x - 10 6. y = 4 4y ...Apr 5, 2021 · In this lesson we’ll look at how to use the slopes of two lines in the Cartesian plane (the xy-plane) to see if the lines are perpendicular, parallel, or neither. Parallel lines have equal slopes and will never intersect each other because they’ll always be the same distance apart. Perpendicular lines have slopes that are negative ... Two lines have the same slope if and only if they are parallel. Two lines are perpendicular if and only if the product of their slopes is -1. Exercises Determine whether MN ⎯⎯ and RS ⎯ are parallel, perpendicular, or neither. Graph each line to verify your answer. 1. M(0, 3), N(2, 4), R(2, 1), S(8, 4) 2. M(-1, 3), N(0, 5), R(2, 1), S(6 ...94. $3.50. PDF. Parallel & Perpendicular Lines (Linear Equations) - Practice / Review:This sorting activity helps your students practice classifying pairs of lines as the same line, parallel lines, perpendicular lines, or neither.*Note- This item is also available as part of a DISCOUNTED bundle: Slope and Graph.94. $3.50. PDF. Parallel & Perpendicular Lines (Linear Equations) - Practice / Review:This sorting activity helps your students practice classifying pairs of lines as the same line, parallel lines, perpendicular lines, or neither.*Note- This item is also available as part of a DISCOUNTED bundle: Slope and Graph.Parallel & perpendicular lines from equation. Writing equations of perpendicular lines. Writing equations of perpendicular lines (example 2) Write equations of parallel & perpendicular lines. Proof: parallel lines have the same slope. Proof: perpendicular lines have opposite reciprocal slopes. Analytic geometry FAQ. Students color the parts of the egg based on whether the lines in the section are parallel, perpendicular, or neither. Coloring fun for bigger kids! The larger packet contains 5 different worksheets, focusing on identifying types of angles, right triangles, lines, line segments, rays, and types of lines.THE parallel line? I can't answer your question because there are infinite lines which don't intersect your line. Any line which has the same slope ...The lines are perpendicular if the slopes have negative reciprocals. Each set of intersecting lines is not a set of perpendicular lines. Web displaying 8 worksheets for parallel …Parallel and Perpendicular Lines. Instructions. • Use black ink or ball-point ... Check your answers if you have time at the end mathsgenie.co.uk. Page 2. 3. 1.Parallel lines have slopes that are the same. All of the lines shown in the graph are parallel because they have the same slope and different y- intercepts. Lines that are perpendicular intersect to form a 90∘ 90 ∘ angle. The slope of one line is the negative reciprocal of the other. We can show that two lines are perpendicular if the ...Determine whether these lines are parallel, perpendicular, or neither. Justify your answer. 13 State whether the lines represented by the equations y = 1. 2 x ...4 In each case find an equation for the line passing through the origin which is also perpendicular to the line joining the two points given. a (4, 3), (–2, –9) b (0, 3), (–10, 8) Extend 5 Work out whether these pairs of lines are parallel, perpendicular or neither. a y = 2x + 3 b y = 3x c y = 4x – 3 y = 2x – 7 2x + y – 3 = 0 4y + x = 2This means the lines are neither parallel nor perpendicular. So the answer is neither. Now that we have a sense of how the slopes of parallel and perpendicular lines are related, let’s try some more challenging examples which combine the ideas of 6.5 with parallel and perpendicular lines. Example 3:Gina Wilson Parrallel And Perpendicular Lines - Displaying top 8 worksheets found for this concept.. Some of the worksheets for this concept are Parallel perpendicular or neither color work gina wilson, Homework 11 parallel and perpendicular lines gina wilson, Parallel and perpendicular lines, Homework 11 parallel and perpendicular lines gina …Geometry Parallel and perpendicular lines Parallel and perpendicular lines Are the lines parallel, perpendicular or intersecting? Parallel lines never intersect. Lines that intersect at 90 degrees are perpendicular. In these worksheets, students identify parallel and perpendicular lines. All worksheets are printable pdf files. Classify the lines:Both lines have a slope m = 3 4 and thus are parallel. Perpendicular lines are lines in the same plane that intersect at right angles ( 90 degrees). Two nonvertical lines in the same plane, with slopes m1 and m2, are perpendicular if the product of their slopes is − 1: m1 ⋅ m2 = − 1. We can solve for m1 and obtain m1 = − 1 m2.Straight-line graphs, parallel/perpendicular, length and area problems Key points • When lines are parallel they have the same gradient. • A line perpendicular to the line with equation y = mx + c has gradient . Examples Example 1 Find the equation of the line parallel to y = 2x + 4 which passes through the point (4, 9). y = 2x + 4 m = 2 y ...Study with Quizlet and memorize flashcards containing terms like 1. parallel, 1. neither, a. neither and more. ... Determine if the following lines are parallel, perpendicular, or neither: y = -7x + 4 y = -7x + 3. 1. perpendicular. 1. Determine if the following lines are parallel, perpendicular, or neither: y = 2/7x - 1 y = -7/2x. About us.Example 2: State true or false using the properties of parallel and perpendicular lines. a.) The letter A has a set of perpendicular lines. b.) The opposite sides of a rectangle are parallel lines. c.) Parallel lines intersect each other at 90°. Solution: Using the properties of parallel and perpendicular lines, we can answer the given ...Parallel & perpendicular lines from equation. Writing equations of perpendicular lines. Writing equations of perpendicular lines (example 2) Write equations of parallel & perpendicular lines. Proof: parallel lines have the same slope. Proof: perpendicular lines have opposite reciprocal slopes. Analytic geometry FAQ.Linear Equations: Transformations, Parallel and Perpendicular . Practice Worksheet Name _____ Algebra 1 Date _____ Block ____ Given . 𝒇𝒇(𝒙𝒙) = 𝒙𝒙 ... Are the graphs of each pair of equations parallel, perpendicular, or neither? 19. 𝑦𝑦= 2𝑥𝑥+ 1 20. 𝑦𝑦= 1 21. Find a line perpendicular to and intersecting it at . 2. Find a line parallel to the y-axis and including the point . 3. In each part, determine whether the two lines are parallel, perpendicular, or neither.Tell whether the lines for each pair of equations are parallel, perpendicular, or neither. ____ 16. 7x – 4y = 4 x – 4y = 3 a. perpendicular b. parallel c. neither. ... Short Answer 19. Suppose you have $20.00 to buy cold cuts for a class picnic. Ham costs $3.99 per pound and turkey costsAnswer: Lines with the same slope are parallel and if the slope of one line is the negative reciprocal of the second line, then they are perpendicular. This quiz focuses on determining whether lines are parallel or perpendicular, based on their respective equations. Parallel nonvertical lines have the same slope, m1 = m2 and different y-intercepts, b1 ≠ b2. Perpendicular lines in a plane are lines that intersect at a right or 90 degree angle. Two nonvertical lines are perpendicular if the ... Test Match Q-Chat Created by sdecatur Teacher Terms in this set (15) y = 1/2x + 2 y = 1/2x -1 Parallel y = 2/3x - 3 y = -3/2x + 2 Perpendicular y = 4x + 1 y = -3 - 1/4x Perpendicular y = 2/3x - 1 y = 2 + 2/3x Parallel y = 2/5x - 1 y = 2 + 3/5x Neither Study with Quizlet and memorize flashcards containing terms like neither, parallel (same slope), parallel (same slope) and more.Expert Answer. Ans 41: Step 1: Given line AB with coordinates of A (-1, -4) and that of B (2, 11) Step 2: Given line CD with coordinates of C (1, 1) and that of D (4, 10) Step 3: Let us calculate slopes of both these lines Slope = m = (y2 - y1)/ (x …. Determine whether AB and CD are parallel, perpendicular, or neither.Note: This worksheet is supported by a flash presentation, under Mausmi’s Math Movies. Mausmi Jadhav Q2: Determine whether the graphs of each pair of equations are parallel, perpendicular or neither. 1. y = 3x + 4 y = 3x + 7 2. y = -4x + 1 4y = x + 3 3. y = 2x - 5 y = 5x - 5 4. y = -1/3x + 2 y = 3x - 5 5. y = 3/5x - 3 5y = 3x - 10 6. y = 4 4y ...Parallel, Perpendicular or Neither Worksheet with answers A-CED.1-2 F-IF.4, 6, 7 This PDF file contains (2) separate assignments.All of the lines shown in the graph are parallel because they have the same slope and different y- intercepts. Lines that are perpendicular intersect to form a \displaystyle {90}^ {\circ } 90∘ -angle. The slope of one line is the negative reciprocal of the other. We can show that two lines are perpendicular if the product of the two slopes is ...Parallel, Perpendicular or Neither (From Points) Riddle This is an 15 question Riddle Practice Worksheet designed to practice and reinforce how to figure out if sets of points create lines that are parallel, perpendicular or neither using slope. This worksheet is perfect for Geometry, Algebra and Algebra 2! The worksheet includes : 15 questions …Use these differentiated worksheets to help KS2 children practise identifying parallel and perpendicular lines in year 3 and to consolidate what they have learned in their Maths lessons. Containing 6 worksheets on parallel and perpendicular lines for KS2, this pack starts with simple worksheets which ask pupils to circle the examples of parallel or …Math Giraffe. 5.0. (95) $3.50. PDF. Parallel & Perpendicular Lines (Linear Equations) - Practice / Review:This sorting activity helps your students practice classifying pairs of lines as the same line, parallel lines, perpendicular lines, or neither.*Note- This item is also available as part of a DISCOUNTED bundle: Slope and Graphing Linear ...Get your free intersecting lines worksheet of 20+ questions and answers. Includes reasoning and applied questions. DOWNLOAD FREE. x. ... By considering the gradients of the two lines, we can decide whether they are parallel, perpendicular or neither. Step-by-step guide: Parallel and perpendicular lines. sunday cryptoquotelucky luciano death photosfs1 fios channelhomes for sale in edgerton ohio Parallel perpendicular or neither worksheet answers zgp prefix bcbs [email protected] & Mobile Support 1-888-750-6043 Domestic Sales 1-800-221-5645 International Sales 1-800-241-6895 Packages 1-800-800-7199 Representatives 1-800-323-4274 Assistance 1-404-209-3347. To determine if two lines are parallel or perpendicular, you have to look at the slopes. For the line y=kx+b, k is the slope. For two lines y=k 1 x+b 1 and y=k 2 X+b 2 , When K 1 =K 2, two lines are parallel; when K 1 =-1/k 2, two lines are perpendicular.It doesn't matter whatever b 1, b 2 are. Hence to save time, you only need to calculate k 1 …. wv inroads login 4 In each case find an equation for the line passing through the origin which is also perpendicular to the line joining the two points given. a (4, 3), (–2, –9) b (0, 3), (–10, 8) Extend 5 Work out whether these pairs of lines are parallel, perpendicular or neither. a y = 2x + 3 b y = 3x c y = 4x – 3 y = 2x – 7 2x + y – 3 = 0 4y + x = 2Parallel and Perpendicular Lines Q 1 : Find the slope of the line passing through the pairs of points and describe the line as rising, falling, horizontal or vertical. a. (2 , 1) , (4 , 5) b. (-1 , 0) , (3 , -5) c. (2 , 1) , (-3 , 1) d. (-1 , 2) , (-1 ,- 5) dekalb county alabama jail inmate rosterwayne state sdn Given Slopes of Two Lines Determine if the Lines are Parallel, Perpendicular, or Neither. 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. These worksheets will produce 10 problems per page. cadillac dts on 20strue game data warzone New Customers Can Take an Extra 30% off. There are a wide variety of options. Study with Quizlet and memorize flashcards containing terms like neither, parallel (same slope), parallel (same slope) and more.Please save your changes before editing any questions. 5 minutes. 1 pt. Determine if the lines are parallel, perpendicular, or neither. Parallel. Perpendicular. Neither. Multiple …Parallel Perpendicular or Neither Worksheet Answer Key with Web the codes lead to multiple choice questions where the students have to determine if the equations given are parallel, perpendicular,. Web in this set of printable worksheets for 3rd grade, 4th grade, and 5th grade kids are required to identify whether the pair of. }