[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-366143-105":59,"doc-detail-366143-en":131},{"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":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","lesson-guide-triangle-congruence-theorems-explained","Lesson Guide - Triangle Congruence Theorems Explained","","Lesson guide that supports a video lesson on triangle congruence theorems, starting with the meaning of congruence and the key question set for reasoning. It explains how corresponding sides and angles determine when two triangles are congruent, even without identical orientation. The guide covers SSS, SAS, ASA, AAS, and HL, including what each theorem requires and how it proves congruence. It also addresses why Angle-Side-Side (and Side-Angle-Side) alone does not guarantee congruence.",{"@graph":69,"@context":123},[70,84,106],{"@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/lesson-guide-triangle-congruence-theorems-explained/366143/",{"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/lesson-guide-triangle-congruence-theorems-explained/366143.png","ImageObject",300,407,{"name":92,"@type":93},"anakgang17","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-09-23",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",17,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What does congruence mean for triangles?","Question",{"text":113,"@type":114},"Two triangles are congruent if their corresponding sides and corresponding angles have the same/equal measure.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"When can the SSS theorem be used?",{"text":118,"@type":114},"Use SSS when three pairs of corresponding sides are congruent to each other; then you can conclude the triangles are congruent.",{"name":120,"@type":111,"acceptedAnswer":121},"Why doesn’t Angle-Side-Side prove triangle congruence?",{"text":122,"@type":114},"Because the measure of the angle between the two congruent sides is unknown, you cannot be sure of the angle’s location.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},366143,1790318678,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":34,"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},962090883568,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Name:    \nLesson Guide  \nThis lesson guide accompanies the following video lesson:  \nTriangle Congruence Theorems Explained  \nKey Questions:  \n• What does congruence mean? ≅  \n• What are the 5 triangle congruence postulates?  \n• Why do these postulates prove congruence?  \n• How do you know which triangle congruence postulate to use?  \nTwo triangles are   if their corresponding sides and angles have the same/equal measure.  \nThis is true even when the triangles do not have the same   .  \nThe Triangle Congruence Theorems:  \nMashup Math LLC | All Rights Reserved | Get More K-12 Math Worksheets [at ](at www.mashupmath.com)[www.mashupmath.com](at www.mashupmath.com) 1  \nSSS stands for    \nThe SSS theorem applies when there are three pairs of corresponding sides that are congruent to each other.  \nIn this case, we can use the SSS triangle congruence theorem to conclude that the triangles are   and that the corresponding sides and corresponding angles have the same   .  \nIn your own words, describe the SSS theorem:  \nMashup Math LLC | All Rights Reserved | Get More K-12 Math Worksheets [at ](at www.mashupmath.com)[www.mashupmath.com](at www.mashupmath.com) 2  \nSAS stands for    \nThe SAS theorem applies when there are twos sets of corresponding sides that are congruent to each other with a corresponding congruent angle in between.  \nIn this case, we can use the SAS triangle congruence theorem to conclude that the triangles are   and that the corresponding sides and corresponding angles have the same   .  \nIn your own words, describe the SAS theorem:  \nMashup Math LLC | All Rights Reserved | Get More K-12 Math Worksheets [at ](at www.mashupmath.com)[www.mashupmath.com](at www.mashupmath.com) 3  \nASA stands for    \nThe ASA theorem applies when there are twos sets of corresponding angles that are congruent to each other with a corresponding congruent side in between.  \nIn this case, we can use the ASA triangle congruence theorem to conclude that the triangles are   and that the corresponding sides and corresponding angles have the same   .  \nIn your own words, describe the ASA theorem:  \nMashup Math LLC | All Rights Reserved | Get More K-12 Math Worksheets [at ](at www.mashupmath.com)[www.mashupmath.com](at www.mashupmath.com) 4  \nAAS stands for    \nThe AAS theorem applies when there are twos sets of consecutive corresponding angles that are congruent to each other with a corresponding congruent side next to the angles..  \nIn this case, we can use the AAS triangle congruence theorem to conclude that the triangles are   and that the corresponding sides and corresponding angles have the same   .  \nIn your own words, describe the AAS theorem:  \nMashup Math LLC | All Rights Reserved | Get More K-12 Math Worksheets [at ](at www.mashupmath.com)[www.mashupmath.com](at www.mashupmath.com) 5  \n* HL only applies to   triangles.  \nHL stands for    \nThe AAS theorem applies when there are twos sets of consecutive corresponding angles that are congruent to each other with a corresponding congruent side next to the angles..  \nIn this case, we can use the HL triangle congruence theorem to conclude that the triangles are   and that the corresponding sides and corresponding angles have the same   .  \nIn your own words, describe the HL theorem:  \nMashup Math LLC | All Rights Reserved | Get More K-12 Math Worksheets [at ](at www.mashupmath.com)[www.mashupmath.com](at www.mashupmath.com) 6  \nAngle-Side-Side or Side-Side-Angle does NOT prove triangle congruence!  \nDiagram:  \nSince we don’t know the measure of the angle between the two congruent sides, we can not be sure of its location.  \nIn your own words, describe why Angle-Side-Side does not prove congruence:  \nMashup Math LLC | All Rights Reserved | Get More K-12 Math Worksheets [at ](at www.mashupmath.com)[www.mashupmath.com](at www.mashupmath.com) 7","cbCaigO7RLVRuhrH","https://ap.wps.com/l/cbCaigO7RLVRuhrH","pdf",1574657,"English","# Key Questions\n# Triangle Congruence Definition\n# The Triangle Congruence Theorems\n## SSS\n## SAS\n## ASA\n## AAS\n## HL\n# Non-Proving Case: Angle-Side-Side","[{\"question\":\"What does congruence mean for triangles?\",\"answer\":\"Two triangles are congruent if their corresponding sides and corresponding angles have the same/equal measure.\"},{\"question\":\"When can the SSS theorem be used?\",\"answer\":\"Use SSS when three pairs of corresponding sides are congruent to each other; then you can conclude the triangles are congruent.\"},{\"question\":\"Why doesn’t Angle-Side-Side prove triangle congruence?\",\"answer\":\"Because the measure of the angle between the two congruent sides is unknown, you cannot be sure of the angle’s location.\"}]","Lesson Guide - Triangle Congruence Theorems Explained | PDF",1790163971,18]