[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-386971-105":59,"doc-detail-386971-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","congruent-triangles-proof-activity-part-i","Congruent Triangles Proof Activity - Part I","","Geometry Unit 5 congruent triangles proof activity, Part I. For each of six problems, identify and diagram the given congruent sides and/or angles using tick marks and arcs, then note any additional congruent parts such as vertical angles, shared sides, or angle relationships from parallel lines. Complete missing proof statements by selecting the correct congruence postulate or theorem (SSS, SAS, ASA, AAS, or HL) to justify the triangle congruence statements provided.",{"@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/congruent-triangles-proof-activity-part-i/386971/",{"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/congruent-triangles-proof-activity-part-i/386971.png","ImageObject",300,407,{"name":92,"@type":93},"Mary Man","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-08","2026-09-24",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",14,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What steps are required for each congruent triangles proof problem?","Question",{"text":113,"@type":114},"Draw the given information with tick marks for congruent sides and arcs for congruent angles, add any other congruent parts you can identify, state the matching congruence postulate/theorem, then fill in the blanks to complete the proof.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"Which congruence postulates or theorems are used in these problems?",{"text":118,"@type":114},"The worksheet calls for using SSS, SAS, ASA, AAS, or HL to prove the triangles are congruent.",{"name":120,"@type":111,"acceptedAnswer":121},"How do vertical angles and parallel lines help in the proofs?",{"text":122,"@type":114},"Vertical angles can be used to establish angle congruence, and parallel lines can create equal alternate interior angles or matching angle pairs to support the triangle congruence reasoning.","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},386971,1790695551,{"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":14,"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":24,"preview_page_count":4},7421720224475,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","Geometry, Unit 5 – Congruent Triangles Proof Activity – Part I Name    \nFor each problem, do the following:  \na. Show the given information in the diagram (using tick marks to show congruent sides and arcs to show congruent angles)  \nb. Show any other congruent parts you notice (from vertical angles, sides shared in common, or alternate interior angles with parallel lines)  \nc. Give the postulate or theorem that proves the triangles congruent (SSS, SAS, ASA, AAS, HL)  \nd. Finally, fill in the blanks to complete the proof.  \n1. Given: BC ≅ DC ; AC ≅ EC Prove: ΔBCA ≅ ΔDCE  \n\n| Statements | Reasons |\n| --- | --- |\n| 1. | 1. Given |\n| 2. | 2. Vertical ∠s Theorem |\n| 3. ΔBCA ≅ ΔDCE | 3. |\n\n2. Given: JK ≅ LK ; JM ≅ LM Prove: ΔKJM ≅ ΔKLM  \n\n| Statements | Reasons |\n| --- | --- |\n| 1. | 1. |\n| 2. | 2. Reflexive Prop. |\n| 3. | 3. |\n\n3. Given: ∠G ≅ ∠I ; FH bisects ∠GFI  \nProve: ΔGFH ≅ ΔIFH  \n\n| Statements | Reasons |\n| --- | --- |\n| 1. ∠G ≅ ∠I ; FH bisects ∠GFI | 1. |\n| 2. ∠GFH ≅ ∠IFH | 2. Def. of   |\n| 3. | 3. Reflexive Prop. |\n| 4. | 4. |\n\nK  \nJ  \nM  \nG  \nF H  \nI  \n4. Given: ∠N and ∠Q are right angles; NO ≅ PQ Prove: ΔONP ≅ ΔPQO  \n\n| Statements | Reasons |\n| --- | --- |\n| 1. ∠N and ∠Q are right angles | 1. |\n| 2. ΔONP and ΔPQO are   triangles | 2. Def. of right triangle |\n| 3. | 3. Reflexive Prop. |\n| 4. NO ≅ PQ | 4. |\n| 5. | 5. |\n\nN  \nO  \nP  \nQ  \n        S T  \n5. Given: ST || RU ; SR || TU  \nProve: ΔSRT ≅ ΔUTR  \n\n| Statements | Reasons |\n| --- | --- |\n| 1. ST || RU | 1. |\n| 2. | 2. If lines ||, alt. int. ∠s ≅ |\n| 3. SR || TU | 3. |\n| 4. ∠SRT ≅ ∠ UTR | 4. |\n| 5. | 5. |\n| 6. | 6. |\n\nR U  \n6. Given: ∠W and ∠Y are right angles; VX ≅ ZX ; X is the midpoint of WY Prove: ΔVWX ≅ ΔZYX  \n\n| Statements | Reasons |\n| --- | --- |\n| 1. ∠W and ∠Y are right angles | 1. |\n| 2. | 2. Def. of right triangle |\n| 3. VX ≅ ZX ; X is the midpoint of WY | 3. |\n| 4. | 4. Def. of midpoint |\n| 5. | 5. |\n\nV Z  \nW X Y","cbCaii5C9NMDro0n","https://ap.wps.com/l/cbCaii5C9NMDro0n","pdf",255652,"English","# Congruent Triangles Proof Activity - Part I\n## Problem 1\n## Problem 2\n## Problem 3\n## Problem 4\n## Problem 5\n## Problem 6","[{\"question\":\"What steps are required for each congruent triangles proof problem?\",\"answer\":\"Draw the given information with tick marks for congruent sides and arcs for congruent angles, add any other congruent parts you can identify, state the matching congruence postulate/theorem, then fill in the blanks to complete the proof.\"},{\"question\":\"Which congruence postulates or theorems are used in these problems?\",\"answer\":\"The worksheet calls for using SSS, SAS, ASA, AAS, or HL to prove the triangles are congruent.\"},{\"question\":\"How do vertical angles and parallel lines help in the proofs?\",\"answer\":\"Vertical angles can be used to establish angle congruence, and parallel lines can create equal alternate interior angles or matching angle pairs to support the triangle congruence reasoning.\"}]","Congruent Triangles Proof Activity - Part I | PDF",1790280169]