[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-662698-105":59,"doc-detail-662698-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","lecture-5-parallel-lines-and-intersecting-lines","Lecture 5 - Parallel Lines and Intersecting Lines","","Lecture 5 explains projection-based geometry concepts focusing on parallel and intersecting lines. It states that parallel lines have no common point, highlights an exception when lines are perpendicular to the FL, and describes a method to confirm parallelism by using an additional view and drawing lines parallel to complete the third view. The lecture then defines intersecting lines as sharing one common point, requires point projections to align in adjacent views, and distinguishes skew lines when alignment fails. It also introduces coincident lines and includes diagrams and symbol-based projections.",{"@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/lecture-5-parallel-lines-and-intersecting-lines/662698/",{"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/lecture-5-parallel-lines-and-intersecting-lines/662698.png","ImageObject",300,407,{"name":92,"@type":93},"Aldword","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-10-28",true,{"@type":102,"interactionType":103,"userInteractionCount":24},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How can you determine whether two lines are parallel using multiple views?","Question",{"text":112,"@type":113},"Even when lines are perpendicular to the FL, draw the 3rd view to check parallelism. If parallel lines are required, use one view to draw the lines parallel, then complete the 3rd view.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What condition confirms that two lines intersect?",{"text":117,"@type":113},"Intersecting lines have exactly one common point, and the projection of those points must be aligned in adjacent views. If the projections align, the lines intersect.",{"name":119,"@type":110,"acceptedAnswer":120},"What does it mean if the projections do not align in adjacent views?",{"text":121,"@type":113},"If the projections of the common-point locations do not align in adjacent views, the lines are skewed rather than intersecting.","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},662698,1793221805,{"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":24,"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":129,"read_time":144},2336478940917,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","10b. Parallel Lines  \n• Parallel lines do not have any common point between them  \n• Parallel lines are seen as parallel in adjacent views, exception to this when the lines are perpendicular to the FL, the lines may or may not be parallel  \n10b. Parallel Lines  \n• To find out if the lines are parallel, even if the lines are perpendicular to the FL, it is best to draw the 3rd view  \n• If it is required to get the lines parallel, then use one view, draw the lines parallel and complete the 3rd view  \n10b. Parallel Lines  \nbH  \naH kH  \nkFaF  \nbF  \njH  \naP  \njF  \nF P  \nkP  \nbP  \njP  \nH  \nF  \n10c. Intersecting Lines  \n• Intersecting lines have one common point between them  \n• The projection of the points must be aligned in adjacent views  \n• If they are, then the lines are intersecting  \n• If not, they are skewed  \n\n| bH |  |  | \u003Cbr>\u003Cbr>\u003Cbr>\u003Cbr>\u003Cbr>|  |  |  |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| eH |  |  |  |  |  |  |  |  |  |  |  |  |\n| a\u003Cbr>H | \u003Cbr>H |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |\n| F\u003Cbr>aF eF | \u003Cbr>|  |  | gPaP |  |  | |  |  |  |  | bP |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  | \u003Cbr>bF F |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  | P | eP  |  |  |  |  |  |  |  |  |\n\n10c. Intersecting Lines  \n• Intersecting lines have one common point between them  \n• The projection of the points must be aligned in adjacent views  \n• If they are, then the lines are intersecting  \n• If not, they are skewed  \neF  \nbH  \neH  \naH  \ngH  \nHF  \ngF aF  \nbF F P  \ngPaP  \neP  \nbP  \n10c. Intersecting Lines  \n• Intersecting lines have one common point between them  \n• The projection of the points must be aligned in adjacent views  \n• If they are, then the lines are intersecting  \n• If not, they are skewed  \neF  \nbH  \neH  \naH  \ngH  \nHF  \ngF aF  \nbF F P  \ngPaP  \neP  \nbP  \n10c. Coincident lines  \n\n| bH\u003Cbr>|  |  | |  |  |\n| --- | --- | --- | --- | --- | --- |\n| \u003Cbr>H |  |  |  |  |  |\n|  |  |  |  |  |  |\n| F |  |  | aP\u003Cbr>|  | bP |\n| \u003Cbr>aF  |  |  |  | |  |\n| \u003Cbr>bF F\u003Cbr>|  |  | P |  |  |\n\n10c. Coincident lines  \n\n| dH\u003Cbr>bH |  |  |  |  | \u003Cbr>|  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- |\n| \u003Cbr>|  |  |  |  |  |  |  |\n| H |  |  |  |  |  |  |  |\n| F |  |  |  |  | cP\u003Cbr>aP |  | dP\u003Cbr>bP |\n| cFaF | \u003Cbr> dF \u003Cbr>bF\u003Cbr>\u003Cbr>|  |  |  |  |  |  |\n|  |  |  |  |  | |  |  |\n|  |  |  |  | F | P |  |  |\n\n11. Location of a line  \nLocate a line // to a given line passing through a point  \nH  \nF  \n\n| aH\u003Cbr>| sH |\n| --- | --- |\n| \u003Cbr>aF | sF\u003Cbr>|\n\nbH  \nbF  \n11. Location of a line  \nLocate a line // to a given line passing through a point  \naH  \nbH  \nkH  \njH  \nsH  \nH F  \nkF  \naF  \nsF  \n jF  \nbF","cbCait8udnpgq9aX","https://ap.wps.com/l/cbCait8udnpgq9aX","pdf",1111073,76,"English","# 10b. Parallel Lines\n## 10b. Parallel Lines - How to identify parallelism\n# 10c. Intersecting Lines\n## 10c. Intersecting Lines - Aligned projections vs skew\n## 10c. Coincident lines\n# 11. Location of a line\n## Location of a line - Constructing a line through a point","[{\"question\":\"How can you determine whether two lines are parallel using multiple views?\",\"answer\":\"Even when lines are perpendicular to the FL, draw the 3rd view to check parallelism. If parallel lines are required, use one view to draw the lines parallel, then complete the 3rd view.\"},{\"question\":\"What condition confirms that two lines intersect?\",\"answer\":\"Intersecting lines have exactly one common point, and the projection of those points must be aligned in adjacent views. If the projections align, the lines intersect.\"},{\"question\":\"What does it mean if the projections do not align in adjacent views?\",\"answer\":\"If the projections of the common-point locations do not align in adjacent views, the lines are skewed rather than intersecting.\"}]","Lecture 5 - Parallel Lines and Intersecting Lines | PDF",192]