[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-462049-105":59,"doc-detail-462049-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","basics-of-geometry-section-11-points-lines-and-planes-lesson","Basics of Geometry - Section 1.1 Points, Lines, and Planes - Lesson","","Study geometry foundations covering undefined terms point, line, and plane, along with how to name and distinguish them. Learn core skills for identifying collinear and coplanar points, visualizing intersections among lines and planes, and sketching scenarios where objects intersect or do not. Includes related measurement and construction goals, absolute value and triangle area examples, coordinate-plane context, unit-conversion practice, and activities using dynamic geometry software to deepen understanding.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/basics-of-geometry-section-11-points-lines-and-planes-lesson/462049/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/basics-of-geometry-section-11-points-lines-and-planes-lesson/462049.png","ImageObject",300,407,{"name":92,"@type":93},"MrHarris58","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-03","2026-09-30",true,{"@type":102,"interactionType":103,"userInteractionCount":52},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What are the undefined terms in geometry and why are they used?","Question",{"text":112,"@type":113},"Point, line, and plane are treated as undefined terms because they have no formal definitions, but there is agreement about what they mean. They are represented using everyday visual models such as dots, arrow-ended lines, and floor/wall-like planes.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How do you name a point, line, and plane?",{"text":117,"@type":113},"A point is represented by a dot and can be named with a letter. A line uses two arrowheads and can be named by any two points on it. A plane has two dimensions and can be named using three non-collinear points.",{"name":119,"@type":110,"acceptedAnswer":120},"How do you determine intersections of lines and planes?",{"text":121,"@type":113},"Use the provided scenarios to describe and sketch how two lines, a line and a plane, or two planes can intersect or not intersect. The activities ask for examples based on the classroom layout (walls, floor, and ceiling).","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},462049,1791165302,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":52,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":145,"preview_page_count":4},687212988360,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","1 Basics of Geometry  \n1.1 Points, Lines, and Planes  \n1.2 Measuring and Constructing Segments  \n1.3 Using Midpoint and Distance Formulas  \n1.4 Perimeter and Area in the Coordinate Plane  \n1.5 Measuring and Constructing Angles  \n1.6 Describing Pairs of Angles  \nChapter Learning Target:  \nUnderstand basics of geometry.  \nChapter Success Criteria:  \n■ I can name points, lines, and planes.  \n■ I can measure segments and angles.  \n■ I can use formulas in the coordinate plane.  \n■ I can construct segments and angles.  \nAlamillo Bridge (p. 53)  \nAlamillo Bridge  \n(p 53)  \nSulfur Hexafluoride (p. 7)  \n| Maintaining Mathematical Proficiency\u003Cbr>Finding Absolute Value\u003Cbr>Example 1 Simplify ∣ −7 − 1∣ .\u003Cbr>∣ −7 − 1∣ = ∣ −7 + (−1)∣ Add the opposite of 1.\u003Cbr>= ∣ −8∣ Add.\u003Cbr>= 8 Find the absolute value.\u003Cbr>∣ −7 − 1∣ = 8\u003Cbr>Simplify the expression.\u003Cbr>1. ∣ 8 − 12∣ 2. ∣ −6 − 5∣ 3. ∣ 4 + (−9)∣\u003Cbr>4. ∣ 13 + (−4)∣ 5. ∣ 6 − (−2)∣ 6. ∣ 5 − (−1)∣\u003Cbr>7. ∣ −8 − (−7)∣ 8. ∣ 8 − 13∣ 9. ∣ −14 − 3∣\u003Cbr>Finding the Area of a Triangle\u003Cbr>Example 2 Find the area of the triangle.\u003Cbr> 5 cm\u003Cbr>\u003Cbr>18 cm\u003Cbr>A = bh Write the formula for area of a triangle.\u003Cbr>= (18)(5) Substitute 18 for b and 5 for h.\u003Cbr>= (90) Multiply 18 and 5.\u003Cbr>= 45 Multiply  and 90.\u003Cbr>The area of the triangle is 45 square centimeters.\u003Cbr>Find the area of the triangle. |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- |\n| 10. | 22 m\u003Cbr>\u003Cbr>14 m | 11.\u003Cbr>7 yd | | 12.\u003Cbr>16 in. | |\n|  |  |  |  | 25 in. |  |\n| 13. ABSTRACT REASONING Describe the possible values for x and y when ∣ x − y ∣ > 0. What does it mean when ∣ x − y ∣ = 0? Can ∣ x − y ∣ \u003C 0? Explain your reasoning. |  |  |  |  |  |\n\nDynamic Solutions available [at BigIdeasMath.com](at BigIdeasMath.com)  \n1  \nMathematical Practices  \nMathematically proficient students carefully specify units of measure.  \nSpecifying Units of Measure  \nCore Concept  \nCustomary Units of Length  \n1 foot = 12 inches  \n1 yard = 3 feet  \n1 mile = 5280 feet = 1760 yards  \nMetric Units of Length  \n1 centimeter = 10 millimeters  \n1 meter = 1000 millimeters  \n1 kilometer = 1000 meters  \nConverting Units of Measure  \nFind the area of the rectangle in square centimeters. Round your answer to the nearest hundredth.  \nSOLUTION  \nUse the formula for the area of a rectangle. Convert the units of length from customary units to metric units.  \nArea = (Length)(Width) Formula for area of a rectangle  \n= (6 in.)(2 in.) Substitute given length and width.  \n= [(6 in.)( im ) ][(2 in.)( im ) ] Multiply each dimension by the conversion factor.= (15.24 cm)(5.08 cm) Multiply.  \n≈ 77.42 cm2 Multiply and round to the nearest hundredth.  \n The area of the rectangle is about 77.42 square centimeters.  \nMonitoring Progress  \nFind the area of the polygon using the specified units. Round your answer to the nearest hundredth.  \n1. triangle (square inches) 2. parallelogram (square centimeters)  \n2 cm  \n3. The distance between two cities is 120 miles. What is the distance in kilometers? Round your answer to the nearest whole number.  \n2 Chapter 1 Basics of Geometry  \n1.1 Points, Lines, and Planes  \nEssential Question How can you use dynamic geometry software  \nto visualize geometric concepts?  \n Using Dynamic Geometry Software  \nWork with a partner. Use dynamic geometry software to draw several points. Also, draw some lines, line segments, and rays. What is the difference between a line, a line segment, and a ray?  \nSample  \n\n| A\u003Cbr>\u003Cbr>| |\n| --- | --- |\n\nUNDERSTANDING MATHEMATICAL TERMS  \nIntersections of Lines and Planes  \nWork with a partner.  \na. Describe and sketch the ways in which two lines can intersect or not intersect. Give examples of each using the lines formed by the walls, floor, and ceiling in  \nyour classroom.  \nb. Describe and sketch the ways in which a line and a plane can intersect or not intersect. Give examples of each using the walls, floor, and ceiling in your classroom.  \nc. Describe and sketch the ways in which two planes can intersect or not intersect. Give example","cbCaijIVa9Vkr0rm","https://ap.wps.com/l/cbCaijIVa9Vkr0rm","pdf",9656860,62,"English","# Basics of Geometry\n## Points, Lines, and Planes\n## Measuring and Constructing Segments\n## Midpoint and Distance Formulas\n## Perimeter and Area in the Coordinate Plane\n## Measuring and Constructing Angles\n## Describing Pairs of Angles\n## Absolute Value\n## Area of a Triangle\n## Mathematical Practices","[{\"question\":\"What are the undefined terms in geometry and why are they used?\",\"answer\":\"Point, line, and plane are treated as undefined terms because they have no formal definitions, but there is agreement about what they mean. They are represented using everyday visual models such as dots, arrow-ended lines, and floor/wall-like planes.\"},{\"question\":\"How do you name a point, line, and plane?\",\"answer\":\"A point is represented by a dot and can be named with a letter. A line uses two arrowheads and can be named by any two points on it. A plane has two dimensions and can be named using three non-collinear points.\"},{\"question\":\"How do you determine intersections of lines and planes?\",\"answer\":\"Use the provided scenarios to describe and sketch how two lines, a line and a plane, or two planes can intersect or not intersect. The activities ask for examples based on the classroom layout (walls, floor, and ceiling).\"}]","Basics of Geometry - Section 1.1 Points, Lines, and Planes - Lesson | PDF",1790763117,156]