Quarter 3 Module 1: Basic Concepts And Terms In Geometry

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7MathematicsQuarter 3 – Module 1:Basic Concepts and Terms inGeometryCO Q3 Mathematics 7 Module 1

Mathematics – Grade 7Alternative Delivery ModeQuarter 3 – Module 1: Basic Concepts and Terms in GeometryFirst Edition, 2020Republic Act 8293, section 176 states that: No copyright shall subsist in any workof the Government of the Philippines. However, prior approval of the government agency oroffice wherein the work is created shall be necessary for exploitation of such work for profit.Such agency or office may, among other things, impose as a condition the payment ofroyalties.Borrowed materials (i.e., songs, stories, poems, pictures, photos, brand names,trademarks, etc.) included in this module are owned by their respective copyright holders.Every effort has been exerted to locate and seek permission to use these materials fromtheir respective copyright owners. The publisher and authors do not represent nor claimownership over them.Published by the Department of EducationSecretary: Leonor Magtolis BrionesUndersecretary: Diosdado M. San AntonioDevelopment Team of the ModuleWriter:Jacqueline C. MarcosEditor:Alfredo T. Ondap, Jr.Reviewer:Reynaldo C. TagalaIllustrator:Jacqueline C. MarcosLayout Artist: Maylene F. GriganaManagement Team: Allan G. FarnazoGilbert B. BarreraArturo D. Tingson Jr.Peter Van C. Ang-ugDonna S. PanesElizabeth G. TorresJudith B. AlbaPrinted in the Philippines by:Department of Education – SOCCSKSARGEN - Region XIIOffice Address:Telefax:E-mail Address:Regional Center, Brgy. Carpenter Hill, City of Koronadal(083) 2288825/ (083)2281893region12@deped.gov.ph

7MathematicsQuarter 3 – Module 1:Basic Concepts and Terms inGeometry

Introductory MessageThis Self-Learning Module (SLM) is prepared so that you, our dear learners,can continue your studies and learn while at home.Activities, questions,directions, exercises, and discussions are carefully stated for you to understandeach lesson.Each SLM is composed of different parts. Each part shall guide you step-bystep as you discover and understand the lesson prepared for you.Pre-tests are provided to measure your prior knowledge on lessons in eachSLM. This will tell you if you need to proceed on completing this module or if youneed to ask your facilitator or your teacher’s assistance for better understanding ofthe lesson. At the end of each module, you need to answer the post-test to selfcheck your learning. Answer keys are provided for each activity and test. We trustthat you will be honest in using these.In addition to the material in the main text, Notes to the Teacher are alsoprovided to our facilitators and parents for strategies and reminders on how theycan best help you on your home-based learning.Please use this module with care. Do not put unnecessary marks on anypart of this SLM. Use a separate sheet of paper in answering the exercises andtests. And read the instructions carefully before performing each task.If you have any questions in using this SLM or any difficulty in answeringthe tasks in this module, do not hesitate to consult your teacher or facilitator.Thank you.

What I Need to KnowThis module was designed and written with you in mind. It is here to help youmaster Basic Concepts and Terms in Geometry. The scope of this module permits itto be used in many different learning situations. The language used recognizes thediverse vocabulary level of students. The lessons are arranged to follow thestandard sequence of the course. But the order in which you read them can bechanged to correspond with the textbook you are now using.After going through this module, you are expected to: represent point, line and plane using concrete and pictorial models (M7GEIIIa-1); andillustrate subsets of a line (M7GE-IIIa-2).1CO Q3 Mathematics 7 Module 1

What I KnowMultiple choice. Read each item carefully. Choose the letter of the best answerand write it on a separate sheet of paper.1. Which of the following does not represent a plane?A. boardB. edge of a notebookC. surface of the tableD. screen of an iPad2. In every line, there are at least how many distinct points?A. 5B. 4C. 3D. 23. Which of the following represents a line?A. dotB. table coverC. envelopD. yarn4. Which of the following represents a point?A. tip of a pinB. penC. peso billD. edge of the ruler5. In every plane, there are at least how many noncollinear points?A. 5B. 4C. 3D. 26. What is the intersection of a plane and a line perpendicular to the plane?A. lineB. planeC. pointD. space7.Which of the following best describes a line?A. Usually represented by a dotB. A flat surfaceC. Can be extended in both directionsD. Has width and thickness2CO Q3 Mathematics 7 Module 1

For numbers 8-11, refer to the illustration on the right.W8. What is the intersection of planes W and G?A. spaceB. pointC. planeD. lineGAB9. Which of the following is a ray in the given figure?A. ray ABB. ray AGC. ray AWD. ray WG10. If A and B are collinear, are they also coplanar?A. yesB. noC. maybeD. cannot be determined11. What is the correct symbol for the intersection of the two planes?A. ABB. ABC. ABD. AB12. WhatA.B.C.D.is the undefined term in geometry that has no dimension?lineplanepointspaceFor numbers 13-15, refer to the illustration on the right.13. What is the intersection of LV and OE?A. lineB. planeC. pointD. space14. What is the common point of LV and OE?A. LB. OC. VD. SLOSEV15. How do you call lines LO and VE?A. concurrent linesB. intersecting linesC. parallel linesD. skew lines3CO Q3 Mathematics 7 Module 1

Lesson1Basic Concepts and Termsin GeometryLooking back at our first drawing as a child, we often remember points, linesand even planes in the form of familiar shapes. These concepts and terms are partof geometry.Geometry is a branch of mathematics that studies the sizes, shapes,position, angles, dimensions of things and the knowledge dealing with spatialrelationship. This is from the Ancient Greek words: “geo” which means “earth” and“-metrein” which means “to measure”. The basic knowledge and concepts will helpus appreciate better the beauty of nature and the things around us.This time, let us dig deeper on these basic concepts and terms in geometry.Let’s go!What’s InLet us recall on the common shapes we have at preschool. Identify them firstbefore answering the questions that follow.Shape 1Shape 2Shape 3Shape 4Questions:1. What do these shapes have in common?2. How many corners does shape 1 have?3. How many corners does shape 2 have?4. How many corners does shape 3 have?5. How many corners does shape 4 have?6. In each shape, what connects one corner to the other?7. How do we call the intersection of one side to the other?4CO Q3 Mathematics 7 Module 1

What’s NewNow, let us familiarize some words related to the lesson through thisanagram. This is an activity in which words are formed by rearranging the letters ofwords or by arranging letters taken at random. Your task is to rearrange thehighlighted letters to form the word described.AnagramDescriptionWord Formed1. NILEIt has no width and no thicknessbut can be extended infinitely inopposite directions.2. TOPINIt has no dimension and usuallyrepresented by a dot.3. NAPLEIt is a flat surface that extendsinfinitely in all directions4. GETSEMNIt is formed when two distinctpoints are connected with a line.5. ARYIt has only one endpoint and anarrowhead which extends infinitelyin one directionWhat is ItIn any mathematical system, definitions are important. Elements andobjects must be defined precisely. However, there are some terms or objects thatare the primitive building blocks of the system and hence cannot be definedindependently of other objects. In geometry, these are point, line, plane, andspace. There are also relationships like between that are not formally defined butare merely described or illustrated.A. UNDEFINED TERMSIn Euclidean Geometry, the geometric terms point, line, and plane are allundefined terms and are purely mental concepts or ideas. However, we can useconcrete objects around us to represent these ideas. Thus, these undefined termscan only be described.5CO Q3 Mathematics 7 Module 1

TermFigure Apoint JlineDm ZplaneAYX DescriptionA point suggests an exactlocation in space.It has no dimension.We use a capital letter toname a point.A line is a set of pointsarranged in a row.It is extended endlessly in bothdirections.It is a one-dimensional figure.Two points determine a line.That is, two distinct points arecontained by exactly one line.We use a lowercase letter orany two points on the line toname the line.A plane is a set of points in anendless flat surface.The following determine aplane:(a) three non-collinear points;(b) two intersecting lines;(c) two parallel lines; or(d) a line and a point not onthe line.We use an uppercase letter,script letter, such as A, orthree points on the plane toname the plane.Notationpoint Aline m orJDplane A,planeXYZorXYZConsider the following illustrations:lCmLines l and m intersect at point C.BASPLine AB and plane M intersect at point A.MRPlanes S and R have PQ in common. Theyintersect at PQ.Q6CO Q3 Mathematics 7 Module 1

Since we have already described the undefined terms, we need thefollowing postulates to serve as guiding rules or assumptions from whichother statements on the undefined terms may be derived.Postulates Two points are contained in exactly one line. Every line contains at least two distinct points. If two points are on a plane, then the line containing these points is also onthe plane. Every[[[ plane contains at least three noncollinear points. (Plane Postulate) Any three points lie in at least one plane and any threenoncollinear points lie in exactly one plane. If two distinct planes intersect, then their intersection is a line.There are some objects around us that could represent a point, lineor a plane.tip of a pencillouvers of a windowcover of a bookObjects that couldrepresent aPOINT1. Tip of a needleObjects that couldrepresent aLINE1. LaserObjects that couldrepresent aPLANE1. blackboard2. The intersection of2. Pen2. wallthe front wall, the3. Intersection of the3. aside wall and thefront wall and theceilingside wall7sheetofintermediate paperCO Q3 Mathematics 7 Module 1

B. OTHER BASIC GEOMETRIC TERMS ON POINTS AND LINESTermIllustrationDescriptioncollinearpoints These are points on the sameline.coplanarpoints/lines These are points/ lines on thesame plane.interestinglines Two or more lines are intersectingif they have a common point.parallellines These are coplanar lines that donot meet.concurrentlines Threeormorelinesareconcurrent if they all intersect atonly one point.skew lines These are lines that do not lie onthe same plane.8CO Q3 Mathematics 7 Module 1

C. SUBSETS OF LINESThe following are some of the subsets of a esegment It is a part of a line that AB or BAorinhas two endpoints.symbols,AB or BA It is a subset of a line buthas one endpoint, andextends in one direction.rayCED Wenameraybyitsendpoint and one of itspoints. Naming a ray willalwaysstartontheendpoint.rayCDorrayCE or insymbols,CDCEorConsider the following illustrations:A line segment XY, as a subset ofline XZ, consists of points X and Y and allthe points between them.XYIf the line to which a line segmentbelongs is given a scale so that it turnsinto the real line, then the length of thesegment can be determined by gettingthe distance between end points.ZGiven the points on the numberline on the left, the length of the followingsegments may be derived.1. AB ( 6) – ( 3) 3 unitsAB-6 -5 -4 -3 -2 -1C0D E12 342. CD 0 – (3) 3 units3. BD ( 3) – (3) 6 units4. BC ( 3) – (0) 3 units5. AC ( 6) – (0) 6 unitsSegments are congruent if theyhave the same length. So, AB and CD, BCand CD, and AC and BD are pairs ofcongruent segments.9CO Q3 Mathematics 7 Module 1

BAThe points A, B, C are on ray AC.However, referring to another ray BC, thepoint A is not on ray BC.CThe points of AB are all the points onsegment AB such that B is between A and C.If JM is extended in the direction ofJCpoint J, a line is formed. Point C is theMcommon endpoint of the two rays.CJ and CM are opposite rays.What’s MoreLet us check your understanding about the basic concepts and termsin geometry by answering the following activities.A. Real-life objects represent a point, line, or a plane. Place each objectin its corresponding column in the table below.hair strandtip of a ballpenelectric wirecorner of a tablesurface of the tableedge of a paperscreen of a smartphoneplywoodthreadintersection of a side wall and the ceilingObjects that couldrepresent aPOINTObjects that couldrepresent aLINE10Objects that couldrepresent aPLANECO Q3 Mathematics 7 Module 1

B. Use the given figure to identify what is being asked.MCJNEADQzh1. What are the points in the interior region of the triangle?2. Give other name(s) for line h.3. Name three (3) line segments on line h.4. Name four (4) rays on line h.5. If E is the midpoint of DN, name a pair of congruent segments.C. The points A, B, C, D, E, F, G, and H are the corners of a box shownbelow. Answer the questions that follow.1. How many lines can be formed bythese points? (Hint: There are morethan 20.)2. What are the lines that containpoint A? (Hint: There are more thanthree lines.)3. Identify the different planes whichcan be formed by these points.(Hint: There are more than six.)4. What are the planes that containline DC?BADCFEHG5. What are the planes that intersectat line BF?11CO Q3 Mathematics 7 Module 1

What I Have LearnedLet’s recap! Identify the geometric term described in each sentence. Choosethe terms from the list below.pointlineplaneopposite raysrayline segmentconcurrent linesintersecting linesparallel linesskew linescollinearcoplanar1. It is a subset of a line with one endpoint and an arrowhead.2. These are lines that are not coplanar.3. It has no dimension.4. Two or more coplanar lines that meet at a common point.5. It is a flat surface.6. Three or more lines that intersect at only one point.7. These are lines that will never meet.8.It is a set of points extended infinitely in both directions.9. It is a subset of a line with two endpoints.10. Points or lines that lie on the same plane.Good job! Now you’re up for the next challenge of this lesson.12CO Q3 Mathematics 7 Module 1

What I Can DoThis section involves real-life application of the basic concepts and terms ingeometry that we have studied. Do what is asked.Direction: Roam around your house and look for objects which represent a point, aline or a plane. For each column, list at least 3 objects not mentionedearlier in the discussion and draw the object.Objects that couldrepresent aPOINTObjects that couldrepresent aLINEObjects that couldrepresent aPLANE1.1.1.2.2.2.3.3.3.Excellent work! You did a good job in applying what you have learned!13CO Q3 Mathematics 7 Module 1

AssessmentMultiple choice. Read each item carefully. Choose the letter of the best answerand write it on a separate sheet of paper.1. Which of the following does not represent a point?A. dotB. edge of a notebookC. intersection of two linesD. tip of a pen2. WhatA.B.C.D.is the geometric term represented by a nylon string?pointlineplanerayFor numbers 3-6, refer to the illustration on the right.3. Which of the following is the name of the plane?A. plane AB. plane BC. plane CD. plane FpFrCBA4. Which of the following is not a point?A. AB. BC. CD. F5. What is the best geometric term for line p and line r?A. skew linesB. parallel linesC. intersecting linesD. concurrent lines6. In theA.B.C.D.given figure, what is A?linepointraysegment7. WhatA.B.C.D.are points that lie on the same line?coplanarcollinearcommon pointpoint of intersection14CO Q3 Mathematics 7 Module 1

For numbers 8-10, refer to the illustration on the right.8. WhatA.B.C.D.is the intersection of plane ZYRX and plane CXRM?line segment ZYline segment YDline segment RXRline segment CM9. Which of the following lines does not contain M?A. line RXB. line RMC. line DMD. line CMYZXDJMC10. What is the intersection of planes ZXCJ, ZYRX, and CMRX?A. line ZXB. line RXC. point RD. point X11. WhatA.B.C.D.is the intersection of two distinct planes?pointlineplaneray12. WhatA.B.C.D.does a rope represent?linepointplaneray13. The top of a table represents what geometric term?A.B.C.D.pointplaneline segmentline14. How do we name the illustration of a ray on the right?A. LVLVB. LVC. LVD. VL15. What are segments with equal length?A. collinear segmentsB. congruent segmentsC. coplanar segmentsD. opposite segments15CO Q3 Mathematics 7 Module 1

Additional ActivitiesLet us try your reasoning power. Answer the following questions and state yourreasons.1. Consider the stars in the night sky. Do they represent points?2. Consider the moon in its fullest form. Would you consider a full moon as arepresentation of a point?3. A point has no dimension. A line has a dimension. How come that a linecomposed of dimensionless points has a dimension?4. A pencil is an object that represents a line. Does a pencil extend infinitely inboth directions? Does a pencil really represent a line?16CO Q3 Mathematics 7 Module 1

CO Q3 Mathematics 7 Module 1What I Know1. B2. D3. D4. A5. C6. C7. C8. D9. A10.A11.D12.C13.C14.D15. CWhat’s More(Continuation)B.1.2.3.4.5.C.1.2.3.4.5.What’s NewWhat’s areStarAnswer to Questions:1. Closed figure/corners/ plane43410Line/ sidePoint/ dot2.3.4.5.6.7.What I HaveLearned1. ray2. skew lines3. point4. intersecting lines5. plane6. concurrent lines7. parallel lines8. line9. line segment10.coplanarpoint J and point Alines DN, DE, ENlines DE, EN, DNrays ED, EN, ND, DNsegments DE and EN28lines AB, AD, AE, AC,AG, AFplanes ABCD, EFGH,ADHE, BCGF, CDHG,ABFE, ABGH, CDEF,ADGF, BCHEplanes ABCD, EFCD,CDHGplanes ABFE, BFGC,BFHD17What I Can DoLearners’answersmay vary depending onavailable objects at homeand choice.1.2.3.4.5.LinePointPlaneSegmentRayWhat’s MoreA. Representation of:1. Point Corner of thetable Tip of a ballpen2. Line Hair strand Intersection ofside wall andceiling Electric wire Edge of a paper thread3. Plane Screen of asmartphone Surface of thetable 15.BBDDCBBCADBABCBAdditionalActivitiesLearners’ answers mayvary.Answer Key

References1. Bernabe, Julieta G., et al, Geometry Textbook for Third Year. SDPublications, Inc. 20092. Department of Education-Bureau of Learning Resources (DepEd-BLR) (2016)Grade 7 Mathematics Learner’s Module. Lexicon Press Inc., Philippines18CO Q3 Mathematics 7 Module 1

For inquiries or feedback, please write or call:Department of Education - Bureau of Learning Resources (DepEd-BLR)Ground Floor, Bonifacio Bldg., DepEd ComplexMeralco Avenue, Pasig City, Philippines 1600Telefax: (632) 8634-1072; 8634-1054; 8631-4985Email Address: blr.lrqad@deped.gov.ph * blr.lrpd@deped.gov.ph

coplanar points/ lines These are po ints/ lines on the same plane. interesting lines Two or more lines are intersecting if they have a common point. parallel lines These are coplanar lines that do not meet. concurrent lines Three or more lines are concurrent if th ey all intersec

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