[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-386929-105":59,"doc-detail-386929-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","triangle-congruence-postulates-lesson-43-cpctc","Triangle Congruence Postulates - Lesson 4.3 - CPCTC","","Triangle Congruence Postulates lesson content explains angle-side relationships and congruence criteria for triangles. It covers the Side-Angle Inequality Postulate, Triangle Exterior Angle Postulate, and the congruence postulates SSS, SAS, ASA, and AAS. The material includes construction prompts, angle validity checks (e.g., SSA vs AAA, and interior angle sets like 45-45-90), and practice problems that ask learners to mark corresponding congruent parts and state which postulate supports each congruence conclusion, including CPCTC.",{"@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/triangle-congruence-postulates-lesson-43-cpctc/386929/",{"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/triangle-congruence-postulates-lesson-43-cpctc/386929.png","ImageObject",300,407,{"name":92,"@type":93},"Mia  ","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-04","2026-09-24",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",21,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How does the Side-Angle Inequality Postulate relate side lengths to opposite angles?","Question",{"text":113,"@type":114},"In a triangle, if one side is longer than another, then the angle opposite the longer side is larger than the angle opposite the shorter side.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What conditions guarantee two triangles are congruent under SSS, SAS, ASA, and AAS?",{"text":118,"@type":114},"SSS requires all three sides congruent, SAS requires two sides and the included angle congruent, ASA requires two angles and the included side congruent, and AAS requires two angles and a non-included side congruent.",{"name":120,"@type":111,"acceptedAnswer":121},"Why do SSA and AAA sometimes fail to determine a unique triangle?",{"text":122,"@type":114},"SSA may not fix a unique triangle because side-angle-side configurations can lead to different possibilities, while AAA only matches angle measures and leaves scale undetermined for congruence without additional information.","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},386929,1790377831,{"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":52,"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},687207024478,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","| Side-Angle Inequality Postulate\u003Cbr>In a triangle, if one side is longer than another side,\u003Cbr>then the angle opposite the longer side is larger than the angle opposite the shorter side.\u003Cbr>(Lesson 4.3) | C\u003Cbr>a\u003Cbr>If c 􀀡 b 􀀡 a, then 􀂑C 􀀡 􀂑B 􀀡 􀂑A\u003Cbr>b\u003Cbr>B A\u003Cbr>c\u003Cbr>|  |\n| --- | --- | --- |\n| Triangle Exterior Angle Postulate The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles. (Lesson 4.3) | | m􀂑D 􀀠 m􀂑B 􀀎 m􀂑A |\n| SSS Congruence Postulate If the three sides of one triangle are congruent to the three\u003Cbr>sides of another triangle, then the triangles are congruent. (Lesson 4.4) | |  |\n| SAS Congruence Postulate If two sides and the included angle of one triangle are\u003Cbr>congruent to two sides and the included angle of another triangle, then the triangles are\u003Cbr>congruent. (Lesson 4.4) | |  |\n| ASA Congruence Postulate If two angles and the included side of one triangle are\u003Cbr>congruent to two angles and the included side of another triangle, then the triangles are\u003Cbr>congruent. (Lesson 4.5) | |  |\n| AAS Congruence Postulate If two angles and a non-included side of one triangle are\u003Cbr>congruent to the corresponding angles and side of another triangle, then the triangles are\u003Cbr>congruent. (Lesson 4.5) | |  |\n\nConstruct a triangle, more than one if possible, using the following:  \na)  \nA B  \nA C  \nB C  \nb) ~~ ~~  \nA B  \nA C  \n C  \nc)  \nA   \nA C  \n C  \nDraw a triangle with the following interior angles 45, 45, 90.  \nWhy did SSA not work?  \nWhy did AAA not work?  \nMark the following triangles given the stated congruent triangle postulate. DEF  \n\n| SSS\u003Cbr>A\u003Cbr>\u003Cbr>B C | E |  |  | SAA\u003Cbr>A\u003Cbr>|\n| --- | --- | --- | --- | --- |\n|  | D | | F |  |\n| ASA A\u003Cbr>\u003Cbr>B C | E |  |  | \u003Cbr>B C ~~ ~~\u003Cbr>D F |\n|  | D | | F |  |\n\nDetermine which triangles are congruent and why?  \nUsing your previous postulates mark congruent angles and sides if they exist and then find the corresponding congruent triangle. State the reason the two triangles are congruent.  \n1 􀀧 OHW 􀀣 􀀧    \nWhich postulate supports the congruence statement?(if not enough info, write not enough info)    \n2. sAB // sCD ( hint: transversal?), sAD 􀀣 sBC , 􀀧 ABC 􀀣 􀀧    \nWhich postulate supports the congruence statement?(if not enough info, write not enough info)    \nD C  \nA B  \n3. sAC 􀀣 sBD, sAD 􀀣 sBC, 􀀧 ADB 􀀣 􀀧    \nWhich postulate supports the congruence statement?    \nD C  \nA B  \n5. sQD 􀀣 sAD, sQU 􀀣 sAU If you construct segment DU, you can show 􀀧QDU 􀀣 􀀧ADU. Which postulate tells you they are congruent?    \nA  \nQ  \nU  \n6. sAB 􀀣 sCD, 􀂑CDB 􀀣 􀂑ABD  \nWhich postulate tells you that 􀀧 ABD 􀀣 􀀧CDB?    \nA  \nC  \nD B  \n10. which postulate supports each congruence statement?  \n􀀧 ABH 􀀣 􀀧 CBD    \n􀀧 HGF 􀀣 􀀧DEF    \n􀀧 HFB 􀀣 􀀧DFB    \nReview:  \nConstruct the 􀀧 ABC so that it is congruent to 􀀧 PSR using ASA  \nS  \nR  \nP  \nConstruct the 􀀧 ABC so that it is congruent to 􀀧 PSR using SSS  \nConstruct the 􀀧 ABC so that it is congruent to 􀀧 PSR using SAS  \nTRIANGLE CONGRUENCE POSTULATES  \n3.2 CPCTC  \n1. 􀀧 ABC 􀀣 􀀧   .  \nWhich postulate supports the congruence statement?    \nA B  \nC D  \nBecause of   both triangles are congruent. Which means  \nsAC 􀀣 sDB, 􀂑CBD 􀀣 􀂑BCA, and 􀂑CAB 􀀣 􀂑BDC  \n| Which postulate supports the congruence statement?   |  |  |\n| --- | --- | --- |\n| B |  |  |\n| A | | E |\n| D\u003Cbr>Because of   both triangles are congruent. Which means\u003Cbr>sAB 􀀣 sED, sBC 􀀣 sDC, 􀂑B 􀀣 􀂑D, and 􀂑DCE 􀀣 􀂑BCA |  |  |\n\n3. sAB 􀁁 sCD, sAB 􀀣 sCD, EC 􀁁 sCD, 􀂑A 􀀣 􀂑D, 􀀧 ABC 􀀣 􀀧    \nWhich postulate supports the congruence statement?    \nD  \nC  \nBecause of   both triangles are congruent. Which sides and angles are congruent?","cbCaicKbHRGQju9b","https://ap.wps.com/l/cbCaicKbHRGQju9b","pdf",929843,"English","# Triangle postulates overview\n## Side-Angle Inequality Postulate\n## Triangle Exterior Angle Postulate\n## SSS, SAS, ASA, AAS congruence postulates\n# Practice and constructions\n## Construct triangles using given side/angle conditions\n## Interior angle triangle 45-45-90 questions\n## Mark congruent parts and identify supporting postulate\n## Review: construct ABC congruent to PSR using ASA, SSS, SAS","[{\"question\":\"How does the Side-Angle Inequality Postulate relate side lengths to opposite angles?\",\"answer\":\"In a triangle, if one side is longer than another, then the angle opposite the longer side is larger than the angle opposite the shorter side.\"},{\"question\":\"What conditions guarantee two triangles are congruent under SSS, SAS, ASA, and AAS?\",\"answer\":\"SSS requires all three sides congruent, SAS requires two sides and the included angle congruent, ASA requires two angles and the included side congruent, and AAS requires two angles and a non-included side congruent.\"},{\"question\":\"Why do SSA and AAA sometimes fail to determine a unique triangle?\",\"answer\":\"SSA may not fix a unique triangle because side-angle-side configurations can lead to different possibilities, while AAA only matches angle measures and leaves scale undetermined for congruence without additional information.\"}]","Triangle Congruence Postulates - Lesson 4.3 - CPCTC | PDF",1790279005,25]