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Includes examples, guided practice, vocabulary checks, and homework-style skill assessments.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/points-lines-and-planes-chapter-1-basics-of-geometry/493609/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/points-lines-and-planes-chapter-1-basics-of-geometry/493609.png","ImageObject",300,407,{"name":42,"@type":43},"dawugda","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-24","2026-10-01",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",9,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What are the undefined terms in geometry and why do they matter?","Question",{"text":63,"@type":64},"Points, lines, and planes are undefined terms. They are not formally defined, so students need general agreement on their meaning to name and draw geometric elements consistently.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How do you define a line segment and a ray in the book’s notation?",{"text":68,"@type":64},"A line segment AB consists of endpoints A and B and all points between them. A ray AB consists of initial point A and all points on the same side of A as point B.",{"name":70,"@type":61,"acceptedAnswer":71},"How is the intersection of two geometric figures defined?",{"text":72,"@type":64},"Two figures intersect if they share one or more points in common. The intersection is the set of points the figures have in common.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},493609,1791032813,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,110,115,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":93,"slug":94},70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},6,"Technology",50,"technology",{"id":106,"doc_module":4,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},7,"Healthcare",40,"healthcare",{"id":111,"doc_module":4,"doc_module_name":25,"category_name":112,"show_sort_weight":113,"slug":114},8,"Research & Report",30,"research-report",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":96,"slug":129},19,"General","general",{"code":4,"msg":82,"data":131},{"doc_id":79,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":106,"language":139,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":12,"update_tm":143,"read_time":144,"preview_page_count":4},3985747870947,"https://ap-avatar.wpscdn.com/davatar_3d24733baf745e90a7e4bdd5f77d97b2","What you should learn  \n GOAL 1 Understand and use the basic undefined terms and defined terms of geometry.  \nSketch the intersections of lines and planes.  \nWhy you should learn it  \n! To name and draw the basic elements of geometry, including lines that intersect, as in the perspective drawing in Exs. 68–72. L  \nPage 1 of 7  \nPoints, Lines, and Planes  \n GOAL 1  USING UNDEFINED TERMS AND DEFINITIONS   \nA definition  uses known words to describe a new word. In geometry, some words, such as point, line, and plane, are undefined terms. Although these words are not formally defined, it is important to have general agreement about what each word means.  \nA point has no dimension. It is usually represented by a small dot.  \nA line extends in one dimension. It is usually represented by a straight line with two arrowheads to indicate that the line extends without end in two directions. In this book, lines are always straight lines.  \nA plane extends in two dimensions. It is usually represented by a shape that looks like a tabletop or wall. You must imagine that the plane extends without end, even though the drawing of a plane appears to have edges.  \nA  \nPoint A Line ¬ or ¯˘AB Plane M or plane ABC  \nA few basic concepts in geometry must also be commonly understood without being defined. One such concept is the idea that a point lies on a line or a plane.  \n Collinear points   Coplanar points  \nare points that lie on the same line.  \nare points that lie on the same plane.  \nEXAMPLE1 Naming CollinearandCoplanar Points   \na. Name three points that are collinear.  \nb. Name four points that are coplanar.  \nc. Name three points that are not collinear.  \nSOLUTION  \na. Points D, E, and F lie on the same line, so they are collinear.  \nb. Points D, E, F, and G lie on the same plane, so they are coplanar. Also, D, E, F, and H are coplanar, although the plane containing them is not drawn.  \nc. There are many correct answers. For instance, points H, E, and G do not lie on the same line.  \n10 Chapter 1 Basics of Geometry  \nAnother undefined concept in geometry is the idea that a point on a line is between two other points on the line. You can use this idea to define other important terms in geometry.  \nConsider the line AB (symbolized by ¯˘AB) .   line    \nThe line segment  or segment AB (symbolized by ÆAB) A B consists of the endpoints A and B, and all points on ¯˘AB segment  \nthat are between A and B.  \nA B  \nThe ray AB (symbolized by Æ˘AB)consists of the  initial point A and all points on ¯˘AB that lie on the same side of A as point B.  \nNote that ¯˘AB is the same as ¯˘BA, and ÆAB is the same as ÆBA . However, Æ˘AB and Æ˘BA are not the same. They have different initial points and extend indifferent directions.  \nIf C is between A and B, then Æ˘CA and Æ˘CB are  opposite rays.  \nray  \nA B  \nray  \nA B  \nopposite rays  \nA C B  \nLike points, segments and rays are collinear if they lie on the same line. So, any two opposite rays are collinear. Segments, rays, and lines are coplanar if they lie on the same plane.  \nEXAMPLE2 Drawing Lines, Segments, and Rays  \nDraw three noncollinear points, J, K, and L. Then draw ¯˘JK , ÆKL and Æ˘LJ .  \nSOLUTION  \nDraw J, K, and L. 2 Draw ¯˘JK. 3 Draw ÆKL. 4 Draw Æ˘LJ.  \nDrawing Opposite Rays  \nEXAMPLE 3  \nDraw two lines. Label points on the lines and name two pairs of opposite rays.  \nSOLUTION  \nPoints M, N, and X are collinear and X is between Mand N. So, Æ˘XM and Æ˘XN are opposite rays.  \nPoints P, Q, and X are collinear and X is between P and Q. So, Æ˘XP and Æ˘XQ are opposite rays.  \n1.2 Points, Lines, and Planes 11  \n GOAL 2  SKETCHING INTERSECTIONS OF LINES AND PLANES   \nTwo or more geometric figures intersect if they have one or more points in common. The intersection of the figures is the set of points the figures have in common.  \nACTIVITY  \nDeveConppintsg  Modeling Intersections  \nUse two index cards. Label them as shown and cut slots halfway along each card.  \n1. What is the intersection of ÆAB and ÆCD? of","cbCaiskItVoAgJnN","https://ap.wps.com/l/cbCaiskItVoAgJnN","pdf",529565,"English","# What you should learn\n## Goal 1 Using undefined terms and definitions\n## Collinear and coplanar points\n## Line segments and rays\n## Opposite rays\n# Goal 2 Sketching intersections of lines and planes\n## Intersections as common points\n## Sketching intersections examples\n## Guided practice and checks","[{\"question\":\"What are the undefined terms in geometry and why do they matter?\",\"answer\":\"Points, lines, and planes are undefined terms. They are not formally defined, so students need general agreement on their meaning to name and draw geometric elements consistently.\"},{\"question\":\"How do you define a line segment and a ray in the book’s notation?\",\"answer\":\"A line segment AB consists of endpoints A and B and all points between them. A ray AB consists of initial point A and all points on the same side of A as point B.\"},{\"question\":\"How is the intersection of two geometric figures defined?\",\"answer\":\"Two figures intersect if they share one or more points in common. The intersection is the set of points the figures have in common.\"}]","Points, Lines, and Planes - Chapter 1 Basics of Geometry | PDF",1790884509,18]