parallel and perpendicular lines worksheet doc Parallel, perpendicular and intersecting lines worksheets are a beneficial resource for students to gain fundamental knowledge of lines and their types. Slopes of parallel and perpendicular lines worksheet doc Author: Mihexucako Jopujumo Subject: View Parallel_and_Perpendicular_Lines_Worksheet. graphing-parallel-and-perpendicular-lines-worksheet 1/4 Downloaded from bigleap. Solution to Q6: No. Notice how at the center, they meet? Find the slope of the line passing through the pairs of points and describe the line as rising, falling, horizontal q6: Identify whether the lines are parallel, perpendicular or intersecting lines. Worksheet by Kuta Software LLC Answers to Parallel and Perpendicular Lines (ID: 1) 1) y = 8 3 x - 52) y = - 5 3 x + 23) y = - 7 5 algebra 1 worksheet 3 6 parallel and perpendicular lines - 100 images - untitled, heard grace algebra 1, holt algebra 5 7a slopes of parallel perpendicular lines worksheet doc pdf, find foot of perpendicular from point 1 3 6 to plane 2x y, for questions 17 18 find the value of x that would chegg Equations - Parallel and Perpendicular Lines Write the slope-intercept form of the equation of t he line described. M B 1MNa8dFe1 EwKit0hg QInnSfTiDnJiLtEeN vANlbgCeRb7rLae F1B. Slopes of parallel and perpendicular lines worksheet doc Author: Mihexucako Jopujumo Subject: Solving Equations Involving Parallel and Perpendicular Lines www. PROPERTIES OF PARALLEL AND PERPENDICULAR LINES WORKSHEET. doc from MATHEMATIC MISC at University of Dhaka. y = 5 – 2x 3. K 12. y = 2x + 4 m = 2 y . Download File PDF Parallel And Perpendicular Lines Answers Parallel And Perpendicular Lines Answers a\‒‒›‹☂†?q¡£¡‹‡†?d . o). Download and print Turtle Diary's Parallel, Perpendicular, Intersecting Lines worksheet. 2- Parallel Lines and Transversals Parallel and Perpendicular Lines Worksheet focuses on determining whether a pair of lines is parallel or perpendicular. to and passes . 7 Z xMkakdJe O lw aiItWh9 tI xnvf 9iCnxi Gtne s LGKecoTmTeZt hrxy G. Unit 3 Parallel and Perpendicular Lines - Learning Targets & I Can Statements. BeaconLC. org©2001 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. G. Parallel and Perpendicular Lines Lesson Summary: Students will be asked to discover the relationship between the slopes of both parallel and perpendicular lines. Parallel and Perpendicular Lines Worksheet Name: _ HW: Review for test on Friday! Date: _ 1. . 10. If we replace each line with parallel lines going through the origin, then the lines remain perpendicular, and their slopes remain unchanged. that passes through point (4, 1), write in point-slope form. Click the picture to take to this worksheet with parallel and perpendicular lines. j) Two lines perpendicular to a third line are _____perpendicular to each other. 6 Worksheet. 3. CCSS: 4. superteacherworksheets. Equations of Parallel and Perpendicular Lines Worksheet Determine if the given pair of lines is parallel, perpendicular or none 3y=3x+15 MATH MONKS -6x + y = 1 2x-2y= x + 5y = 2 4 Write the slope-intercept form of the equation of the line described E] through -5) parallel to = -2x - 5 through (5, -5) parallel toy = - through (l, 3) algebra 1 worksheet 3 6 parallel and perpendicular lines - 100 images - untitled, heard grace algebra 1, holt algebra 5 7a slopes of parallel perpendicular lines worksheet doc pdf, find foot of perpendicular from point 1 3 6 to plane 2x y, for questions 17 18 find the value of x that would chegg Math Worksheets Name: _____ Date: _____ … So Much More Online! Please visit: www. Write and graph the equation that goes through given point A that is parallel to the original line. 2 Identifying Lines and Angle Relationships 17 B 10/20. perpendicular. Equations - Parallel and Perpendicular Lines Write the slope-intercept form of the equation of t he line described. edu on September 16, 2021 by guest [DOC] Graphing Parallel And Perpendicular Lines Worksheet Recognizing the pretension ways to get this book graphing parallel and perpendicular lines worksheet is additionally useful. Live worksheets > English > Math > Geometry > Perpendicular, parallel and intersecting lines Perpendicular, parallel and intersecting lines drop down menu to choose the correct types of lines The two slopes are equal , the two lines are parallel. 2. m1 = ( 7 - 5 ) / ( -2 - (-2) ) m2 = ( 13 - 1 ) / ( 5 - 5 ) The two slopes are both undefined since the denominators in both m1 and m2 are equal to zero. (4) All rectangles are squares. Example 3: algebra 1 worksheet 3 6 parallel and perpendicular lines - 100 images - untitled, heard grace algebra 1, holt algebra 5 7a slopes of parallel perpendicular lines worksheet doc pdf, find foot of perpendicular from point 1 3 6 to plane 2x y, for questions 17 18 find the value of x that would chegg Kuta software slopes of parallel and perpendicular lines 0 l2r0 i1f1 a 8k hu0t ja p hs0o1f htw5azrdem 6l 4l wcpp t 1aslzlp tr vijg phqt hs9 6rmehsle grwvpekdbj r vm ca mdfej swkibtyh e 2ignlf bi2nki9tzec 1adlog pesbkroab q1n4 4 worksheet by kuta software llc answers to writing equations of parallel and perpendicular lines id. Parallel and Perpendicular Lines . A 10/17 3. algebra 1 worksheet 3 6 parallel and perpendicular lines - 100 images - untitled, heard grace algebra 1, holt algebra 5 7a slopes of parallel perpendicular lines worksheet doc pdf, find foot of perpendicular from point 1 3 6 to plane 2x y, for questions 17 18 find the value of x that would chegg Parallel, Perpendicular or Intersecting Lines Worksheet About This Worksheet: We review the concept of parallel, perpendicular and intersecting line pairs. download Free Sample Example And Format Templates word pdf excel doc xls. S Construct parallel lines through the given points. Keywords: Name: Super Teacher Worksheets - www. k5learning. Parallel and Perpendicular Lines worksheet. Interiors on Same Side Converse If two lines are cut by a transversal and the interior angles on the same side of the transversal are supplementary, the lines are . YouTube. The Geogebra activity below helps underscore the fact that the distance from a point to a line is the length of the perpendicular segment from the point to the line. Worksheet 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. Construct a perpendicular line to each point on the following lines: 4. Find a line perpendicular to and intersecting it at . 1) x y 2) x y Solving Equations Involving Parallel and Perpendicular Lines www. Parallel Lines Perpendicular Lines Intersecting Lines For more worksheet you can log on to www. 40 5. Find slopes of lines, classify parallel and perpendicular lines, and use slope to solve real-life problems VOCABULARY The slope Of a nonvertical line is the ratio of the vertical change (the rise) to the horizontal change (the run). A Worksheet by Kuta Software LLC Algebra 1 ID: 1 Name_____ Date_____ Period____ ©a d2l0 V1v14 xK xuxt KaS YS1okf0trw a0rde3 3L1LRCu. 2- Parallel Lines and Transversals Worksheet by Kuta Software LLC Geometry Graphing Parallel and Perpendicular Lines Name_____ Date_____ ©i S2o0K1h9u QKaustTay vSsoofXtfwragrdem iLCLbCa. 1) y = 4x + 7 (─2, ─9) _____ _____ Slopes of parallel and perpendicular lines worksheet doc . Online reading & math for K-5 www. pdf . 148 - 150 (#2-13, 18-25, 27-29, 35-40) Completed: Chapter 3 section 2: Angles formed by Parallel Lines and Transversals 3. Name: _ Date: _ Hour: _ Parallel and Perpendicular Slopes Worksheet Given the following slopes Determine whether the lines are parallel, perpendicular or neither. 3 Proving Lines Parallel 18 B 10/22 1. Parallel Perpendicular. Chapter 3. (2) All rectangles are parallelograms. Draw the perpendicular bisectors for each of the following segments: 1. 1) x y Parallel and Perpendicular Lines . Start now! Parallel and Perpendicular Lines REVIEW. B If two parallel lines are cut by a transversal, then the alternate exterior angles are congruent. The opposite slope of the line in the equation because perpendicular lines have opposite slopes. h) Two lines parallel to a third line are _____parallel to each other. L. y=-4x-4 y = −4x−4. SHOW ALL WORK . 1) through: (3, 0), parallel to y = 2 3 x + 1 2) through: (4, 1), parallel to y = − 1 2 x + 2 3) through: (−1, −1), parallel to y = −2x − 4 4) through: (−4, −5), parallel to y = −2x − 5 Alternate Exterior Angles Converse If two lines are cut by a transversal and the alternate exterior angles are congruent, the lines are . isb. Common Core Alignment. Our large collection of math worksheets are a great study tool for all ages. 4 answers Sep 02, 2019 · Some of the worksheets below are Hyperbolic Functions Worksheet, Hyperbolic Functions definition, Finding derivatives and integrals of hyperbolic functions, Graphs of hyperbolic functions, the formulae of the basic inverse hyperbolic functions, proof, examples with several examples. Main content: Parallel lines, perpendicular lines, intersecting lines Other contents: straight lines, lines Add to my workbooks (0) Download file pdf Add to Google Classroom Add to Microsoft Teams Share through Whatsapp algebra 1 worksheet 3 6 parallel and perpendicular lines - 100 images - untitled, heard grace algebra 1, holt algebra 5 7a slopes of parallel perpendicular lines worksheet doc pdf, find foot of perpendicular from point 1 3 6 to plane 2x y, for questions 17 18 find the value of x that would chegg graphing-parallel-and-perpendicular-lines-worksheet 1/4 Downloaded from bigleap. 6. Graphing Parallel And Perpendicular Lines Worksheet Doc Graph from parallel and perpendicular lines worksheet algebra 1 answers , source:mypalate. 1) y = 4x + 7 (─2, ─9) _____ _____ Determine whether the lines are parallel, perpendicular or neither. parallel. Lines and points are the basic building blocks of most geometrical shapes, and it is necessary to learn about their types and properties. 7. k) Two planes parallel to the same line are _____ parallel to each other. I can identify skew, parallel, and perpendicular lines. . Selection File type icon File name Description Size Revision Time User; ĉ: Lesson3-2Exploration. Perpendicular and parallel lines worksheet This page shows how to draw a perpendicular to a point on a line with compass and straight or ruler. Parallel and Perpendicular Lines Worksheet . E I gARlRlS rrciRgThrtXsJ QroeEsbemr\vjeYdn. we were unable to retrieve the document for viewing," refresh your browser. In each part, determine whether the two lines are parallel, perpendicular, or neither. Parallel and Perpendicular Lines Worksheet. Note: Matching arrow symbols indicate that lines are parallel. Now consider two lines, L. com Parallel, Intersecting, and Perpendicular A B C D Parallel Lines AB and CD are parallel lines. y = x + 4. 25) through: (-4, -3) The two slopes are equal , the two lines are parallel. An attachment in an email or through the mail as a hard copy, as an instant download. Parallel & Perpendicular Lines. Keywords: Parallel and perpendicular lines worksheet algebra 1 answers perpendicular lines intersect at right angles to one another. 1) y Math Worksheets Name: _____ Date: _____ … So Much More Online! Please visit: www. Multiple Choice. I need help finding a pdf file, or the Key for a book from 2014 titled "All Things Algrebra" by Gina Wilson. 2 Use Parallel Lines and Transversals Notes Key. Lesson 3-4 notes and worksheet. Parallel lines have slopes that are equal. Proofs with Perpendicular Lines. Printable step-by-step instructions The above animation is available as step by step printable algebra 1 worksheet 3 6 parallel and perpendicular lines - 100 images - untitled, heard grace algebra 1, holt algebra 5 7a slopes of parallel perpendicular lines worksheet doc pdf, find foot of perpendicular from point 1 3 6 to plane 2x y, for questions 17 18 find the value of x that would chegg Parallel and Perpendicular Lines Lesson Summary: Students will be asked to discover the relationship between the slopes of both parallel and perpendicular lines. Step 2. to the line that passes through the points (5, 2) and (8, -1) in slope-intercept form. co. algebra 1 worksheet 3 6 parallel and perpendicular lines - 100 images - untitled, heard grace algebra 1, holt algebra 5 7a slopes of parallel perpendicular lines worksheet doc pdf, find foot of perpendicular from point 1 3 6 to plane 2x y, for questions 17 18 find the value of x that would chegg ©e HKYuntLax MSXoCfMtTwHafr oe2 JL2L1CM. • A line perpendicular to the line with equation y = mx + c has gradient . i) Two lines skew to a third line are _____skew to each other. Equations of parallel lines worksheet 3 we start to look at the actual behind the scenes equation behind all of these lines. S k aA2lslG Fr1iIghhEtfsM 8rMejs5eir1vNeDdJ. 1 y x corresponding 2 y x alternate exterior 3. If the two lines are parallel, find the value of k. that are perpendicular to each other. Straight-line graphs, parallel/perpendicular, length and area problems Key points • When lines are parallel they have the same gradient. docx from MATH 5271/5272 at Chippewa Valley High School. I can identify the angles formed when a transversal cuts two parallel lines. Find the equation of a straight line is passing through (2, 3) and parallel to the line 2x - y + 7 = 0. Part 2: Writing equation of perpendicular lines . 1) through: (3, 0), parallel to y = 2 3 x + 1 2) through: (4, 1), parallel to y = − 1 2 x + 2 3) through: (−1, −1), parallel to y = −2x − 4 4) through: (−4, −5), parallel to y = −2x − 5 3. ) Find the slope of a line . Examples Example 1 Find the equation of the line parallel to y = 2x + 4 which passes through the point (4, 9). A7: The slope because parallel lines have the same slope. 2 Use Parallel Lines and Transversals Notes. net Page 4 of 5 Save this file and use it offline, by simply clicking on the colored area. Teacher Decision Check Point: If students are able to answer the questions and everyone has at least 2 parallel lines (perpendicular lines) on their graph then students are ready to move on. r Worksheet #11 Parallel and Perpendicular lines The two slopes are equal , the two lines are parallel. 1 and 3. J Worksheet by Kuta Software LLC Graphing Lines Name_____ Parallel and Perpendicular Lines Find the slope of a line parallel to each given line. In other words, angle between them is right angle (90 angle. and . ©e Z2t0 h1Z1 k qK UuNtraS ZSZo HfRtqw na cr 6e5 eL KLSC Z. 1 Identify Pairs of Lines/Angles Parallel Lines Parallel Postulate Perpendicular Postulate Skew Lines Parallel Planes Diagram with a cube/box Transversals Angles formed by transversals Corresponding Angles Alternate Interior Angles Alternate Exterior Angles Consecutive Interior- (Same Side Interior) Angles 3. Two lines in a plane are parallel if they do not intersect and they have the same slope. Compare the slopes. Parallel and 3 Perpendicular Lines 3. Perpendicular Lines: Lines that . Practice. b h KMEamdze3 bwHi2tqhi LIknmfbianYigt3eS 0AElqg9eDblrOaB q27. This worksheet can be found in every textbook and your teacher will probably include it in every lesson. 2) ©U rKru VthaL wS7o5futWwjacrje1 aLLLeCV. in slope intercept. Write the equation . Parallel and Perpendicular Lines REVIEW. They . Which statement is false? (1) All parallelograms are quadrilaterals. H 9. Also the two lines are horizontal e. Free Online Alevel, GCSE, Secondary, 11+ Maths Resources, Past Exam Papers, Worksheets, Specimen, Solution Videos, Online Test, Online Self-Assessment GCSE Parallel and Perpendicular Lines Worksheet Book Free Consultation Worksheet by Kuta Software LLC Geometry Graphing Parallel and Perpendicular Lines Name_____ Date_____ ©i S2o0K1h9u QKaustTay vSsoofXtfwragrdem iLCLbCa. equations of lines worksheet 2 Equations Of Parallel And Perpendicular Lines Worksheet . algebra 1 worksheet 3 6 parallel and perpendicular lines - 100 images - untitled, heard grace algebra 1, holt algebra 5 7a slopes of parallel perpendicular lines worksheet doc pdf, find foot of perpendicular from point 1 3 6 to plane 2x y, for questions 17 18 find the value of x that would chegg View TestReview Slope. ASSIGNMENT: pg. −y = 4 x + 2 2. Parallel Lines Review. Click here for a detailed description of all parallel and crossline worksheets. The slopes are the same and the intercepts are different, so the lines are parallel. (3) All squares are rhombuses. 1 Identify Pairs of Lines and Angles Notes Key. ) Write the equation of a line that is . J R vM ca MdFej Swkibtyh e 2IGnlf bi2nki9tZec 1ADlog pesbKrOab q1n. algebra 1 worksheet 3 6 parallel and perpendicular lines - 100 images - untitled, heard grace algebra 1, holt algebra 5 7a slopes of parallel perpendicular lines worksheet doc pdf, find foot of perpendicular from point 1 3 6 to plane 2x y, for questions 17 18 find the value of x that would chegg I can write equations of lines that are either parallel or perpendicular to each other. The topic mainly focuses on concepts like alternate angles, same-side angles, and corresponding angles. Drawing Parallel Lines Go through our printable worksheet that trains learners of grade 4 and grade 5 in drawing parallel lines using both a ruler and a grid. Name: Date: Determine if these pairs of lines are parallel, perpendicular or neither: 1) y = − 4 x − 4. Name: _ Date: _ Hour: _ Parallel and Perpendicular Slopes Worksheet Given the following slopes parallel. 3 Proving Lines Parallel Worksheet: 3. J 11. 2 Angle Relationships and Parallel Lines Worksheet: 3. What best describes the relationship between the lines with equations and ? A) perpendicular B) parallel C) same line D) neither parallel nor perpendicular 21. In addition to this, the set also contains practice worksheets on determining whether two lines are parallel or perpendicular, using points, slopes and equations. Gina Wilson All Things Algebra Unit 3 Parallel And Perpendicular Lines Answer Key : 8 7 5 6 P Perpendicular Transversal Theorem In A Plane, If A Line Is Perpendicular To One Of The Two Parallel Lines, Then It Is Perpendicular To The Other. 4 Worksheet by Kuta Software LLC AAT - Graphing Name_____ Worksheet #6 - Parallel and Perpendicular Lines Date_____ Period____ Perpendicular lines. In this lesson, learners first complete an assessment task involving parallel and perpendicular lines in the coordinate plane. 1) y = 4x + 7 (─2, ─9) _____ _____ What best describes the relationship between the lines with equations and ? A) perpendicular B) parallel C) same line D) neither parallel nor perpendicular 20. Some of the worksheets for this concept are find the measure of the indicated angle that makes lines u proving. 4-4-Worksheet by Kuta Software LLC Answers to Writing Equations of Parallel and Perpendicular Lines (ID: 1) 1) y Parallel and perpendicular lines worksheet 3. 5 with parallel and perpendicular lines. Step 1. Line 1: 7 y + 1 = 7 xLine 2: x + 5 = y . 4 -1 parallel to y x 10 through. This set of free worksheets is specially designed for students of grade 4 through high school. Their product is 1. algebra 1 worksheet 3 6 parallel and perpendicular lines - 100 images - untitled, heard grace algebra 1, holt algebra 5 7a slopes of parallel perpendicular lines worksheet doc pdf, find foot of perpendicular from point 1 3 6 to plane 2x y, for questions 17 18 find the value of x that would chegg Parallel And Perpendicular Lines Worksheet. The slopes of the two lines are 7 and (3k + 2). Slopes of parallel and perpendicular lines worksheet doc . Perpendicular distance of a point from a line – GeoGebra Materials. doc View Download: Lesson 3-2 Exploration 52k: v. Write the equation in slope 1. 2 : Jan 15, 2010, 9:13 PM 3. A variety of pdf exercises and word problems will help improve the skills of . Construct a perpendicular line from each point off the line 7. Worksheet by Kuta Software LLC-2-Write the point-slope form of the equation of the line described. 1) x y Paul Pearcy / Chapter 3 Parallel and Perpendicular Lines. So the answer is neither. 1. Block Date Topic Homework 16 B 10/16. A 10/21 3. View Parallel_and_Perpendicular_Lines_Worksheet. Classifying Equations of Parallel and Perpendicular Lines. 1 Identifying Lines and Angles. ©0 L2r0 i1F1 A 8K Hu0t ja p HS0o1f htw5aZrdem 6L 4L wCP. G Sec 3. These parallel and perpendicular worksheets are an excellent resource for children in 5th, 6th, 7th grade, 8th grade, 9th grade and 10th grade. 13. 2 1 parallel to y 1 2 x. -1-Find the slope of each line. 5. Write the equation in slope intercept form of the line parallel and line perpendicular to given line through given point. V 8. Students also identify parallel and perpendicular lines in two dimensional figures. Construct an equilateral triangle. com Equation of Parallel or Perpendicular Lines Write an equation of the line that passes through the given point and is Which quadrilateral must have diagonals that are congruent and perpendicular? (1) rhombus (3) trapezoid (2) square (4) parallelogram. l) Two planes parallel to the same plane are . There are various choices for getting the doc. 1Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines . This means the lines are neither parallel nor perpendicular. Parallel parking might be difficult, but finding parallel lines is fairly simple. R 2 fM3aYd3eu Tw 2i Mt5h k bI1ngf Ii Dnwietxeq RAWlVg2eIb sr NaH B1 7. Postulate (Slopes of parallel lines) : In a coordinate plane, two lines are parallel if and only if they have the same slope. Date: IMPORTANT : Parallel and Perpendicular Lines Parallel Lines: Lines that run in the same direction and never cross. Worksheet by kuta software llc math 1 parallel and perpendicular lines practice name id. We make completing any Algebra 1 Worksheet 3 6 Parallel And Perpendicular Lines easier. EffortlessMath. Parallel and perpendicular lines worksheet kuta software An answer key is provided as well as the full work for all problems on the sheet. The students will use the knowledge discovered and Cabri to find missing coordinates of a parallelogram and the missing coordinate of a rectangle. P t 1AslZlP tr vijg PhQt hs9 6rMeHsle GrWvPekdB. Extra Practice begins on page Parallel Lines have the same slope Perpendicular Lines have. h Y WAvlKlD vrhisg[hHt`sG UrmeQsqeIrbvQehdX. The two lines are vertical lines and therefore parallel. C U 3ASl1lL Qr3i Rguh Nt2s E srIe Ys0e Ir XvYePd2. 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. Find a line parallel to the y-axis and including the point . 1 Identify Pairs of Lines and Angles Practice Worksheet. If the following equations of two lines are parallel, then find the value of k. Given a pair of lines determine if the are parallel perpendicular or intersectin geometry worksheets and writing equations questions revision slopes complete guide mashup math practice 3 7 find x intercept y for each equation linear horizontal vertical game high school teaching line angles final day 5 Given A Pair Of Lines Determine If The Are Parallel Perpendicular… Read More » Unit 3 Syllabus: Ch 3 Parallel and Perpendicular Lines . i f wAtlal w xrqi Sg Thbt6sV or QePsVeqrsv gezd8. 4. 1 Identify Pairs of Lines and Angles Notes. mathebook. com Parallel and perpendicular lines Grade 3 Geometry Worksheet Determine if the lines, segments, or rays are parallel, perpendicular or neither. It works effectively by creating two congruent triangles and then drawing a line between their vertices. teaching them to identify, draw and determine parallel and perpendicular lines. I can apply parallel line theorems and postulates to solve problems. doc View Download . Familiarize students of grade 4 with parallel and perpendicular lines by first enabling them to differentiate between these two lines with this pdf worksheet. For Teachers 9th - 12th Standards. The two slopes are equal , the two lines are parallel. Rewrite the equations in slope-intercept form and determine the slope of each. y=x+4 y = x+4. form of the line parallel and line perpendicular to given line through given point. d P kAclHlI orSi0gshOt5st IraevsWe1rdvbexdt. Download unit 3 parallel and perpendicular gina wilson document. 0 Worksheet by Kuta Software LLC Kuta Software - Infinite Geometry Name_____ Parallel Lines and Transversals Date_____ Period____ Traverse through this array of free printable worksheets to learn the major outcomes of angles formed by parallel lines cut by a transversal. parallel and perpendicular lines worksheet doc