[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-489583-105":59,"doc-detail-489583-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","mathematics-the-vocabulary-of-geometry","Mathematics - The Vocabulary of Geometry","","This educational document provides a structured overview of geometric vocabulary, specifically focusing on the classification and properties of triangles. It covers various triangle types, including equilateral, isosceles, scalene, acute-angled, right-angled, and obtuse-angled triangles. Each category is defined by its unique geometric characteristics, such as side lengths, angle measurements, and lines of symmetry. Additionally, the resource explains the fundamental concept of line symmetry, serving as a comprehensive review aid for students preparing for GCSE Mathematics assessments.",{"@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/mathematics-the-vocabulary-of-geometry/489583/",{"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/mathematics-the-vocabulary-of-geometry/489583.png","ImageObject",300,407,{"name":92,"@type":93},"BigDaveOnline","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-04","2026-10-01",true,{"@type":102,"interactionType":103,"userInteractionCount":39},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What are the defining characteristics of an equilateral triangle?","Question",{"text":112,"@type":113},"An equilateral triangle has three equal sides, three equal angles each measuring 60°, and three lines of symmetry.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How is line symmetry defined in the context of 2-D shapes?",{"text":117,"@type":113},"A shape has line symmetry if one half is a mirror image of the other, with the division occurring along a line of symmetry or mirror line.",{"name":119,"@type":110,"acceptedAnswer":120},"What distinguishes an isosceles triangle from other types?",{"text":121,"@type":113},"Isosceles triangles are characterized by having two equal sides, two equal angles, and exactly one line of symmetry.","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},489583,1792951676,{"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":39,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":8,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":81,"preview_page_count":4},962090896214,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","GCSE  \n  Mathematics: The vocabulary of geometry  \nTriangles and quadrilaterals  \nCheck that you can:  \n• recognise when a shape is a triangle  \n• recognise when a shape is a quadrilateral  \n• understand symmetry in 2-D shapes.  \n| Types of triangle |  |  |\n| --- | --- | --- |\n| You need to know and memorise the special names and properties of four types of triangle.\u003Cbr>Equilateral triangles\u003Cbr>All equilateral triangles have:\u003Cbr>• three equal sides\u003Cbr>• three equal angles, each measuring 60°\u003Cbr>• three lines of symmetry. |  | Scalene triangles\u003Cbr>All scalene triangles have:\u003Cbr>• three sides, each of a different length • three angles, each of a different size • no lines of symmetry.\u003Cbr>Acute-angled triangles\u003Cbr>All acute-angled triangles have three acute angles.\u003Cbr>Right-angled triangles\u003Cbr>All right-angled triangles have:\u003Cbr>• one right-angle\u003Cbr>• two acute angles.\u003Cbr>\u003Cbr>Obtuse-angled triangles\u003Cbr>All obtuse-angled triangles have:\u003Cbr>• one obtuse angle\u003Cbr>• two acute angles. |\n| | |  |\n| These dashes indicate that Lines of symmetry\u003Cbr>the sides are of equal length |  |  |\n| Isosceles triangles\u003Cbr>All isosceles triangles have:\u003Cbr>• two equal sides\u003Cbr>• two equal angles\u003Cbr>• one line of symmetry.\u003Cbr>| |  |\n| Remember!\u003Cbr>A shape has line symmetry if one half of a shape is a mirror image of the other half of the shape. The line that divides the two halves of a symmetrical shape is called the line of symmetry (or mirror line) . |  |  |","cbCaiby8MUodW426","https://ap.wps.com/l/cbCaiby8MUodW426","pdf",1449684,"English","# Types of Triangle\n## Equilateral Triangles\n## Scalene Triangles\n## Acute-angled Triangles\n## Right-angled Triangles\n## Obtuse-angled Triangles\n## Isosceles Triangles\n# Understanding Symmetry","[{\"question\":\"What are the defining characteristics of an equilateral triangle?\",\"answer\":\"An equilateral triangle has three equal sides, three equal angles each measuring 60°, and three lines of symmetry.\"},{\"question\":\"How is line symmetry defined in the context of 2-D shapes?\",\"answer\":\"A shape has line symmetry if one half is a mirror image of the other, with the division occurring along a line of symmetry or mirror line.\"},{\"question\":\"What distinguishes an isosceles triangle from other types?\",\"answer\":\"Isosceles triangles are characterized by having two equal sides, two equal angles, and exactly one line of symmetry.\"}]","Mathematics - The Vocabulary of Geometry | PDF",1790825038]