[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-386863-105":59,"doc-detail-386863-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","gc_triangle_congruence_expressions_extra_practice-extra-practice","GC_Triangle_Congruence_Expressions_Extra_Practice - Extra Practice","","Triangle Congruence explains how congruent triangles imply congruent corresponding parts, and how to match parts using the order of letters in congruence statements. It summarizes the valid proof properties—SSS, SAS, ASA, and HL—and notes that AAS is an acceptable variation of ASA. Examples demonstrate each property step-by-step, followed by practice problems asking whether given triangle pairs are congruent and which congruence property justifies the answer, with a separate answers section.",{"@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/gc_triangle_congruence_expressions_extra_practice-extra-practice/386863/",{"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/gc_triangle_congruence_expressions_extra_practice-extra-practice/386863.png","ImageObject",300,407,{"name":92,"@type":93},"Fans","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-09-24",true,{"@type":102,"interactionType":103,"userInteractionCount":52},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What does it mean when two triangles are congruent?","Question",{"text":112,"@type":113},"If ∆ABC ≅ ∆XYZ, then all six corresponding pairs of parts are congruent. The correspondence follows the letter order in the congruence statement.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"Which triangle congruence properties can be used to prove triangles are congruent?",{"text":117,"@type":113},"SSS, SAS (in that order), ASA, and HL. AAS is an acceptable variation of ASA.",{"name":119,"@type":110,"acceptedAnswer":120},"How can you prove two triangles are congruent using only three pairs of parts?",{"text":121,"@type":113},"Show that three congruencies match a valid congruence property (such as SSS, SAS, ASA, or HL). Once congruence is established, the remaining corresponding parts are also 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},386863,1790718236,{"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":52,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":81,"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":39,"preview_page_count":4},5909892330395,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","TRIANGLE CONGRUENCE  \nIf two triangles are congruent, then all six of their corresponding pairs of parts are also congruent. In other words, if ∆ABC ≅ ∆XYZ, then all the congruence statements at right are  \nA  \nB C  \nX  \nY  \n\\#11  \nZ  \ncorrect. Note that the matching parts follow the order of the letters as written in the triangle congruence statement. For example, if A is first in one statement and X is first in the other, then A always corresponds to X in congruence statements for that relationship or figure.  \nAB  ! XY BC ! YZAC ! XZ  \n!A \" !X  \n!B \" !Y  \n!C \" !Z  \nYou only need to know that three pairs of parts are congruent (sometimes in a certain order) to prove that the two triangles are congruent. The Triangle Congruence Properties are: SSS (Side-Side-Side), SAS (Side-Angle-Side; must be in this order), ASA (Angle-Side-Angle), and HL (Hypotenuse-Leg) . AAS isan acceptable variation of ASA.  \nThe four Triangle Congruence Properties are the only correspondences that maybe used to prove that two triangles are congruent. Once two triangles are know to be congruent, then the other pairs of their corresponding parts are congruent. In this course, you may justify this conclusion with the statement \"congruent triangles give us congruent parts. \" Remember: only use this statement after you have shown the two triangles are congruent.  \nC  \nA  \nT  \nD  \nO  \nG  \nExample 1  \nIn the figure at left, CA ! DO , CT ! DG , and AT! OG . Thus, !CAT \" !DOG because of SSS. Now that the triangles are congruent, it is also true that !C \" !D , !A \" !O , and !T \" !G .  \nExample 2      \nIn the figure at right, RD ! CP , ∠D ≅ ∠P, and ED ! AP . Thus ∆RED ≅ ∆CAP because of SAS. Now RE ! CA , ∠R ≅ ∠C, and ∠E ≅ ∠A.  \nA  \nR  \nD  \nE P C  \nO  \nX B  \nExample 3  \nIn the figure at left, ∠O ≅ ∠A, OX ! AR , and ∠X ≅ ∠R. Thus, ∆BOX ≅  ∆CAR because of  ASA. Now ∠B ≅ ∠C, BO ! CA , and BX ! CR .  \n28 Extra Practice  \nExample 4  \nIn the figure at right, there  are two right angles (m∠N = m∠Y = 90˚) and MO ! KE , and ON ! EY . Thus, ∆MON ≅ ∆KEY because of HL, so MN ! KY , ∠M ≅ ∠K, and ∠O ≅ ∠E.  \nM N Y K  \nExample 5  \nIn the figure ∠S ≅ ∠Q, SR ! QR , and !SRT\" !QRU because of vertical angles. Thus ∆SRT ≅ ∆QRU by ASA.  \nBriefly explain if each of the following pairs of triangles are congruent or not. If so, state the Triangle Congruence Property that supports your conclusion.  \n2.  \nH    \nG J  \nI  \nK  \n5.  \n8.  \nL N  \nK M  \n11.  \nB  \nA  \nD  \n3.  \n6.  \n9.  \nP Q  \nO  \nS  \nR  \nE  \nF  \n12.  \nE  \nG  \nI  \nGEOMETRY Connections 29  \n13.  \nQ  \nR  \n39˚  \n112˚  \nP  \nJ  \nK  \nL  \n14.  \nB  \nE  \n15.  \nW  \nY  \nAnswers  \n1. ∆ABC ≅ ∆DEF 2. ∆GIH ≅ ∆LJK by SAS. 3. ∆PNM ≅ ∆PNO by ASA. by SSS.  \n4. QS ! QS , so 5. The triangles are not 6. ∆ABC ≅ ∆DFE by ∆QRS ≅ ∆QTS by HL. necessarily congruent. ASA or AAS.  \n7. GI ! GI , so 8. Alternate interior 9. Vertical angles ≅ at 0,∆GHI ≅ ∆IJG by SSS. angles = used twice, so so ∆POQ ≅ ∆ROS  \n∆KLN ≅ ∆NMK by by SAS.  \nASA.  \n10. Vertical angles and/or 11. No, the length of each 12. Pythagorean Theorem, alternate interior angles hypotenuse [is different. so](is different. so) ∆EGH ≅ ∆IHG =, so by SSS.  \n∆TUX ≅ ∆VWX  \nby ASA.  \n13. Sum of angles of 14. AF + FC = FC + CD, 15. XZ ! XZ , so  \ntriangle = 180˚, but so ∆ABC ≅ ∆DEF by ∆WXZ ≅ ∆YXZ  \nsince the equal angles SSS. by AAS.  \ndo not correspond, the  \ntriangles are not  \nconguent.  \n30 Extra Practice","cbCaijYFi2VB3tOL","https://ap.wps.com/l/cbCaijYFi2VB3tOL","pdf",412031,"English","# Triangle Congruence Properties\n## Proving Congruent Triangles\n## Example Problems\n## Extra Practice\n## Answers","[{\"question\":\"What does it mean when two triangles are congruent?\",\"answer\":\"If ∆ABC ≅ ∆XYZ, then all six corresponding pairs of parts are congruent. The correspondence follows the letter order in the congruence statement.\"},{\"question\":\"Which triangle congruence properties can be used to prove triangles are congruent?\",\"answer\":\"SSS, SAS (in that order), ASA, and HL. AAS is an acceptable variation of ASA.\"},{\"question\":\"How can you prove two triangles are congruent using only three pairs of parts?\",\"answer\":\"Show that three congruencies match a valid congruence property (such as SSS, SAS, ASA, or HL). Once congruence is established, the remaining corresponding parts are also congruent.\"}]","GC_Triangle_Congruence_Expressions_Extra_Practice - Extra Practice | PDF",1790277530]