[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-523075-105":59,"doc-detail-523075-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","the-triangle-inequality-theorem-the-triangle-inequality-theorem","The Triangle Inequality Theorem - The Triangle Inequality Theorem","","Practice worksheet for the Triangle Inequality Theorem in triangle side measures. Students determine whether given three numbers can represent the lengths of a triangle, marking Yes/No for multiple sets. A second section provides two side lengths and asks for the allowable range of the third side, expressed as inequalities. Includes numbered problems with solutions guided by the theorem’s constraints.",{"@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/the-triangle-inequality-theorem-the-triangle-inequality-theorem/523075/",{"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/the-triangle-inequality-theorem-the-triangle-inequality-theorem/523075.png","ImageObject",300,407,{"name":92,"@type":93},"Pentious","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-17","2026-10-08",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 do you decide whether three numbers can be the side lengths of a triangle?","Question",{"text":112,"@type":113},"Check the triangle inequality conditions so each side length is less than the sum of the other two. If the set satisfies this, mark Yes; otherwise mark No.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What does the worksheet ask for in problems with two given side lengths?",{"text":117,"@type":113},"It asks for the range of possible measures of the third side, written as an inequality for x.",{"name":119,"@type":110,"acceptedAnswer":120},"Why are the answers for the third side written as inequalities (e.g., 4 \u003C x \u003C 14)?",{"text":121,"@type":113},"Because the triangle inequality allows a continuous set of third-side lengths; the inequality captures all values that form a valid triangle with the two given sides.","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},523075,1791511403,{"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":14,"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":24,"preview_page_count":4},1374404730887,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","Kuta Software-Infinite Geometry Name___________________________________  \nThe Triangle Inequality Theorem Date________________ Period____  \nState if the three numbers can be the measures of the sides of a triangle.  \n1) 7, 5, 4 2) 3, 6, 2  \n3) 5, 2, 4 4) 8, 2, 8  \n5) 9, 6, 5 6) 5, 8, 4  \n7) 4, 7, 8 8) 11, 12, 9  \n9) 3, 10, 8 10) 1, 13, 13  \n11) 2, 15, 16 12) 10, 18, 10  \nTwo sides of a triangle have the following measures. Find the range of possible measures for the third side.  \n13) 9, 5 14) 5, 8  \n15) 6, 10 16) 6, 9  \n17) 11, 8 18) 14, 11  \nKuta Software-Infinite Geometry Name___________________________________  \nThe Triangle Inequality Theorem Date________________ Period____  \nState if the three numbers can be the measures of the sides of a triangle.  \n1) 7, 5, 4 2) 3, 6, 2  \nYes No  \n3) 5, 2, 4 4) 8, 2, 8  \nYes Yes  \n5) 9, 6, 5 6) 5, 8, 4  \nYes Yes  \n7) 4, 7, 8 8) 11, 12, 9  \nYes Yes  \n9) 3, 10, 8 10) 1, 13, 13  \nYes Yes  \n11) 2, 15, 16  \nYes  \n12) 10, 18, 10  \nYes  \nTwo sides of a triangle have the following measures. Find the range of possible measures for the third side.  \n13) 9, 5 14) 5, 8  \n4 \u003C x \u003C 14 3 \u003C x \u003C 13  \n15) 6, 10 16) 6, 9  \n4 \u003C x \u003C 16 3 \u003C x \u003C 15  \n17) 11, 8 18) 14, 11  \n3 \u003C x \u003C 19 3 \u003C x \u003C 25  \nCreate your own worksheets like this one with Infinite Geometry. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaioZYKAiX2aSC","https://ap.wps.com/l/cbCaioZYKAiX2aSC","pdf",22383,"English","# The Triangle Inequality Theorem\n## Determine if three side measures form a triangle\n## Find the possible range for the third side","[{\"question\":\"How do you decide whether three numbers can be the side lengths of a triangle?\",\"answer\":\"Check the triangle inequality conditions so each side length is less than the sum of the other two. If the set satisfies this, mark Yes; otherwise mark No.\"},{\"question\":\"What does the worksheet ask for in problems with two given side lengths?\",\"answer\":\"It asks for the range of possible measures of the third side, written as an inequality for x.\"},{\"question\":\"Why are the answers for the third side written as inequalities (e.g., 4 \\u003c x \\u003c 14)?\",\"answer\":\"Because the triangle inequality allows a continuous set of third-side lengths; the inequality captures all values that form a valid triangle with the two given sides.\"}]","The Triangle Inequality Theorem - The Triangle Inequality Theorem | PDF",1791426469]