[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-366150-105":59,"doc-detail-366150-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","guide-to-geometry-proofs-triangle-practice","Guide to Geometry Proofs - Triangle Practice","","This lesson guide provides structured practice for students learning to construct geometric proofs involving congruent triangles. It features step-by-step examples that demonstrate the use of fundamental geometric principles, including the definition of bisected segments, vertical angle congruence, base angle theorems for isosceles triangles, and the application of triangle congruence postulates like SAS and AAS. The content is designed to assist learners in mastering the logical flow required for two-column proofs in high school geometry.",{"@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/guide-to-geometry-proofs-triangle-practice/366150/",{"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/guide-to-geometry-proofs-triangle-practice/366150.png","ImageObject",300,407,{"name":92,"@type":93},"anakgang17","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-04","2026-09-23",true,{"@type":102,"interactionType":103,"userInteractionCount":56},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What geometric postulate is used to prove that triangle GFK is congruent to triangle HFJ?","Question",{"text":112,"@type":113},"The SAS (Side-Angle-Side) postulate is used, based on the sides created by the bisecting lines and the vertical angles at point F.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How is the triangle BAE proven to be congruent to triangle CDE?",{"text":117,"@type":113},"The proof uses the AAS (Angle-Angle-Side) congruence theorem, following the establishment of isosceles triangle properties and vertical angle congruence.",{"name":119,"@type":110,"acceptedAnswer":120},"What is the significance of the CPCTC reason in the provided proofs?",{"text":121,"@type":113},"CPCTC stands for 'Corresponding Parts of Congruent Triangles are Congruent,' and it is used to prove that specific line segments or angles are equal after the triangles themselves have been proven congruent.","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},366150,1790360215,{"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":56,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":24,"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":144,"preview_page_count":4},962090883568,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Name:    \nLesson Guide  \nThis lesson guide accompanies the following video lesson:  \nPractice with Geometry Proofs  \nPractice Proof \\#1  \nPro Tip: Used colored pens/pencils and highlighters to help you label the diagrams!  \n\n| STATEMENTS | REASONS |\n| --- | --- |\n|  |  |\n|  |  |\n|  |  |\n|  |  |\n\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  \nPractice Proof \\#2  \n| STATEMENTS | REASONS |\n| --- | --- |\n|  |  |\n|  |  |\n|  |  |\n|  |  |\n|  |  |\n\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  \nPractice Proof \\#3  \n| STATEMENTS | REASONS |\n| --- | --- |\n|  |  |\n|  |  |\n|  |  |\n|  |  |\n|  |  |\n|  |  |\n|  |  |\n\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  \nAnswer Key  \n\\#1  \n\\#2  \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  \n\\#3  \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","cbCaickfeDiecwZB","https://ap.wps.com/l/cbCaickfeDiecwZB","pdf",858366,"English","# Practice with Geometry Proofs\n## Triangle Congruence Proof #1\n## Triangle Congruence Proof #2\n## Triangle Congruence Proof #3","[{\"question\":\"What geometric postulate is used to prove that triangle GFK is congruent to triangle HFJ?\",\"answer\":\"The SAS (Side-Angle-Side) postulate is used, based on the sides created by the bisecting lines and the vertical angles at point F.\"},{\"question\":\"How is the triangle BAE proven to be congruent to triangle CDE?\",\"answer\":\"The proof uses the AAS (Angle-Angle-Side) congruence theorem, following the establishment of isosceles triangle properties and vertical angle congruence.\"},{\"question\":\"What is the significance of the CPCTC reason in the provided proofs?\",\"answer\":\"CPCTC stands for 'Corresponding Parts of Congruent Triangles are Congruent,' and it is used to prove that specific line segments or angles are equal after the triangles themselves have been proven congruent.\"}]","Guide to Geometry Proofs - Triangle Practice | PDF",1790163978,13]