[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-386022-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-386022-en":131},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","triangle-proofs-sss-sas-asa-aas-geometry-smart-packet-unit-4-triangles-part-1","Triangle Proofs (SSS, SAS, ASA, AAS) - Geometry SMART Packet - Unit 4 Triangles (Part 1)","","Geometry SMART Packet Unit 4 focuses on triangle congruence and writing proofs using common postulates. It covers SSS, SAS, ASA, and AAS, and emphasizes that AAA or SSA cannot establish triangle congruence. The packet guides students through setting up proofs with statements and reasons, listing key triangle properties and definitions such as reflexive property, vertical angles, midpoints, angle bisectors, perpendicular bisectors, parallel-line angle relationships, and the third angle theorem. Practice problems strengthen these proof methods.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/triangle-proofs-sss-sas-asa-aas-geometry-smart-packet-unit-4-triangles-part-1/386022/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/triangle-proofs-sss-sas-asa-aas-geometry-smart-packet-unit-4-triangles-part-1/386022.png","ImageObject",300,407,{"name":42,"@type":43},"Asher","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-10","2026-09-24",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",72,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"Which congruence postulates are used in this packet to prove two triangles are congruent?","Question",{"text":63,"@type":64},"The packet uses SSS, SAS, ASA, and AAS.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"Why can’t AAA or SSA be used to prove triangles congruent?",{"text":68,"@type":64},"The packet states that triangles cannot be proved congruent using AAA or SSA.",{"name":70,"@type":61,"acceptedAnswer":71},"How do students set up a triangle proof?",{"text":72,"@type":64},"List the givens as the Intro, then write the proof using a statement-and-reason structure, using only information from the given.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},386022,1790379053,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,110,115,120,123,127],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":93,"slug":94},70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},6,"Technology",50,"technology",{"id":106,"doc_module":4,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},7,"Healthcare",40,"healthcare",{"id":111,"doc_module":4,"doc_module_name":25,"category_name":112,"show_sort_weight":113,"slug":114},8,"Research & Report",30,"research-report",{"id":116,"doc_module":4,"doc_module_name":25,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":25,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":25,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":128,"doc_module":4,"doc_module_name":25,"category_name":129,"show_sort_weight":96,"slug":130},19,"General","general",{"code":4,"msg":82,"data":132},{"doc_id":79,"user_id":133,"nickname":42,"user_avatar":134,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":140,"language":141,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":12,"update_tm":145,"read_time":146,"preview_page_count":26,"preview_urls":147},687197207639,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Unit 4: Triangles (Part 1)  \nGeometry SMART Packet  \nTriangle Proofs (SSS, SAS, ASA, AAS)  \nStudent:   Date:   Period:    \nStandards  \nG.G.27 Write a proof arguing from a given hypothesis to a given conclusion.  \nG.G.28 Determine the congruence of two triangles by using one of the five congruence techniques (SSS, SAS, ASA, AAS, HL), given sufficient information about the sides and/or angles of two congruent triangles.  \nSSS (Side, Side, Side)  \nSAS (Side, Angle, Side)  \nASA (Angle, Side, Angle)  \nAAS (Angle, Angle, Side)  \nNote: We can NOT prove triangles with AAA or SSA!!  \nHow to set up a proof:  \nStatement  \nIntro: List the givens  \n9 Most Common Properties, Definitions & Theorems for Triangles   \n\n| 1. Reflexive Property: AB = BA When the triangles have an angle or side in common\u003Cbr>| 6. Definition of a Midpoint Results in two segments being congruent\u003Cbr>|\n| --- | --- |\n| 2. Vertical Angles are Congruent When two lines are intersecting\u003Cbr>| 7. Definition of an angle bisector Results in two angles being congruent\u003Cbr>|\n| 3. Right Angles are Congruent When you are given right trianglesand/or a square/ rectangle\u003Cbr>| 8. Definition of a perpendicular bisector\u003Cbr>Results in 2 congruent segments and right angles.\u003Cbr>|\n| 4. Alternate Interior Angles of Parallel Lines are congruent When the givens inform you that two lines are parallel\u003Cbr>| 9. 3rd angle theorem\u003Cbr>If 2 angles of a triangle are 􀀣 to 2 angles of another triangle, then the 3rd angles are 􀀣\u003Cbr>|\n| 5. Definition of a segment bisector Results in 2 segments being congruent\u003Cbr>| Note: DO NOT ASSUME ANYTHING IF IT IS NOT IN THE GIVEN |\n\nDirections: Check which congruence postulate you would use to prove that the  \ntwo triangles are congruent.  \n\n| 1.\u003Cbr>| |\n| --- | --- |\n| 2.\u003Cbr>| |\n| 3.\u003Cbr>| |\n| 4.\u003Cbr>| |\n| 5.\u003Cbr>| |\n\nPractice. Fill in the missing reasons  \n6. Given: YLF 􀀣 FRY, RFY 􀀣 LFY Prove: 􀁕 FRY 􀀣 􀁕 FLY  \n| Statement | Reason |\n| --- | --- |\n| 1. YLF 􀀣 FRY |  |\n| 2. RFY 􀀣 LFY |  |\n| 3. FY 􀀣 FY |  |\n| 4. 􀁕 FRY 􀀣􀁕 FLY |  |\n\n7. Given:  LT 􀀣 TR , ILT 􀀣 ETR, IT || ER Prove: 􀁕 LIT 􀀣 􀁕 TER  \n| Statement | Reason |\n| --- | --- |\n| 1. LT 􀀣 TR |  |\n| 2. ILT 􀀣 ETR |  |\n| 3. IT || ER |  |\n| 4. LTI 􀀣 ERT |  |\n| 5. 􀁕 LIT 􀀣 􀁕 TER |  |\n\n8. Given: C is midpoint of BD  \nAB 􀁁 BD  \nBD 􀁁 DE  \nProve: 􀁕ABC 􀀣 􀁕 EDC  \n| Statement |  |  | Reason |\n| --- | --- | --- | --- |\n| \u003Cbr>1. C is midpoint of BD |  |  |  |\n| 2. | AB 􀁁 BD and BD 􀁁 DE |  |  |\n| 3. | BC 􀀣 CD |  |  |\n| 4. | 􀂑BCA 􀀣 􀂑ECD |  |  |\n| 5. | 􀂑ABC and 􀂑EDCare right angles |  |  |\n| 6. | 􀂑ABC 􀀣 􀂑EDC |  |  |\n| 7. 􀀧ABC 􀀣 􀀧EDC\u003Cbr>9. Given: BA 􀀣 ED\u003Cbr>C is the midpoint of BEand AD\u003Cbr>Prove: 􀁕ABC 􀀣 􀁕 DEC\u003Cbr>|  |  |  |\n| Statement |  |  | Reason |\n| 1. BA 􀀣 ED |  |  |  |\n| \u003Cbr>2. C is the midpoint of BE and |  | AD |  |\n| 3. BC 􀀣 EC |  |  |  |\n| 4. AC 􀀣 DC |  |  |  |\n| 5. 􀀧ABC 􀀣 􀀧DEC |  |  |  |\n\n10. Given: BC 􀀣 DA  \nAC bisects 􀂑BCD  \nProve: 􀁕ABC 􀀣 􀁕 CDA  \n| Statement | Reason |\n| --- | --- |\n| 1. BC 􀀣 DA |  |\n| 2. AC bisects 􀂑BCD |  |\n| 3. 􀂑BCA 􀀣 􀂑DCA |  |\n| 4. AC 􀀣 AC |  |\n| 5. 􀀧ABC 􀀣 􀀧CDA |  |\n\nPractice. Write a 2-column proof for the following problems.  \n11.  \n12. Given: C is the midpoint of BD and AE Prove:   \n13. Given: AB 􀀣 CB, BD is a median of AC Prove: 􀀧ABD 􀀣 􀀧CBD  \nRegents Practice  14. Which condition does not prove that two triangles are congruent?  \n(1)  (2)  (3)  (4)  \n15. In the diagram of  and  below,  ,  , and  .  \nWhich method can be used to prove ?  \n(1) SSS (2) SAS (3) ASA (4) HL  \n16. In the accompanying diagram of triangles BAT and FLU,  and  .  \nWhich statement is needed to prove ?  \n(1)  (2)  (3)  (4)   \n17. In the accompanying diagram,  bisects  and .  \nWhat is the most direct method of proof that could be used to prove ?  \n(1) (2) (3)   \n(4)","cbCailakQTfublwu","https://ap.wps.com/l/cbCailakQTfublwu","pdf",468748,13,"English","# Unit 4: Triangles (Part 1)\n## Geometry SMART Packet\n## Triangle Congruence (SSS, SAS, ASA, AAS)\n## Standards (G.G.27, G.G.28)\n## Key Properties, Definitions & Theorems for Triangles\n## Practice: Identify congruence postulate\n## Practice: Fill in missing reasons (6-10)\n## Practice: Write a 2-column proof (11-13)\n## Regents Practice (14-17)","[{\"question\":\"Which congruence postulates are used in this packet to prove two triangles are congruent?\",\"answer\":\"The packet uses SSS, SAS, ASA, and AAS.\"},{\"question\":\"Why can’t AAA or SSA be used to prove triangles congruent?\",\"answer\":\"The packet states that triangles cannot be proved congruent using AAA or SSA.\"},{\"question\":\"How do students set up a triangle proof?\",\"answer\":\"List the givens as the Intro, then write the proof using a statement-and-reason structure, using only information from the given.\"}]","Triangle Proofs (SSS, SAS, ASA, AAS) - Geometry SMART Packet - Unit 4 Triangles (Part 1) | PDF",1790271809,33,[148,152],{"page_no":22,"url":149,"width":150,"height":151},"https://res-academy.cache.wpscdn.com/upload/kdocshare/2026-11-08/f03916cbc8f1a5ddf85833953a6383d6.webp",983,1272,{"page_no":26,"url":153,"width":154,"height":155},"https://res-academy.cache.wpscdn.com/upload/kdocshare/2026-11-08/8797bd6be408c8d9e8726754d50b2c07.webp",982,1270]