[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-386928-105":59,"doc-detail-386928-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-geometry-rules-and-theorems","Congruent Triangles - Geometry Rules and Theorems","","Congruent triangles are defined as triangles with the same size and shape, meaning one can be perfectly overlapped with another without gaps or overlaps. The document explains what the congruence symbol “≅” means and how corresponding angles and sides determine congruency. It presents major congruence postulates and theorems, including SSS, SAS, ASA, AAS, and the right-triangle RHS case, and emphasizes CPCT as the key principle for concluding equal corresponding parts.",{"@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-geometry-rules-and-theorems/386928/",{"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-geometry-rules-and-theorems/386928.png","ImageObject",300,407,{"name":92,"@type":93},"Rhys","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-09-24",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",12,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What does it mean when two triangles are congruent?","Question",{"text":113,"@type":114},"Two triangles are congruent when they have the same shape and size, so one can be perfectly overlapped with the other. This requires equality of corresponding angles and sides.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What are the four main triangle congruence rules?",{"text":118,"@type":114},"The document lists SSS, SAS, ASA, and AAS. Each rule states specific sets of equal sides and angles that guarantee the triangles are congruent.",{"name":120,"@type":111,"acceptedAnswer":121},"How does CPCT help in proving triangle congruence?",{"text":122,"@type":114},"CPCT states that if two triangles are congruent, then their corresponding parts—both angles and sides—are equal. It is the principle used to conclude equality after establishing congruence.","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},386928,1790718776,{"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":81,"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":39,"preview_page_count":4},687207024643,"https://ap-avatar.wpscdn.com/davatar_3d24733baf745e90a7e4bdd5f77d97b2","Paraphrasing the text: In geometry, two triangles are considered congruent if they have the same shape and size. There are various theorems and postulates that help determine whether two triangles are congruent or not. These include: 1 . Side-Side-Side (SSS) Congruence Postulate 2 . Side-Angle-Side (SAS) Congruence Postulate 3 . Angle-Side-Angle (ASA) Congruence Postulate 4 . Angle-Angle-Side (AAS) Congruence Postulate Additionally, there are specific theorems for right triangles: 1 . Hypotenuse-Leg (HL) Theorem 2 . Leg-Acute (LA) Angle Theorem 3 . Hypotenuse-Acute (HA) Angle Theorem 4 . Leg-Leg (LL) Theorem Given text here was rewritten using the IB method to increase burstiness. Here's the rewritten text: Congruence of triangles is a fundamental concept in geometry that allows us to compare different shapes and sizes. It's all about finding the conditions under which two triangles are exactly the same in size and shape. When we say that two triangles are congruent, it means they can be overlapped with each other perfectly, without any gaps or overlaps. Imagine having two triangles that fit together like puzzle pieces – if you can place one on top of the other and they match up perfectly, then those triangles are said to be congruent. This is what we mean by congruency in mathematics. The symbol used to represent congruency is ≅ . For example, if triangle ABC is congruent to triangle DEF, we write △ABC≅△DEF. But what does it mean for two triangles to be congruent? It means they have the same corresponding angles and sides. In other words, if you can draw a line connecting the corresponding points on both triangles, those lines will be straight and parallel. Now, let's talk about some of the key rules that help us prove the congruency between two triangles. We have SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), RHS (Right angle-Hypotenuse-Side), and CPCT (Corresponding Parts of Congruent Triangles) . In the SSS rule, we check if all three sides of a triangle are equal to the corresponding three sides of another triangle. If they are, then it satisfies the condition of SSS. For example, in the figure below, we can see that AB = QR, BC = RP, and CA = PQ. This means that ΔABC≅ΔQRP. Similarly, in the SAS rule, we check if two sides and the angle included between them are equal. If they are, then it satisfies the condition of SAS. In the ASA rule, we check if two angles and a side are equal. If they are, then it satisfies the condition of ASA. AAS is similar to ASA, but instead of two angles and a side, we have two sides and an angle that are equal. RHS (Right angle-Hypotenuse-Side) is another important rule that helps us prove the congruency between two triangles. It's specifically used when one triangle has a right angle and the other has a hypotenuse of the same length. CPCT (Corresponding Parts of Congruent Triangles) is perhaps the most important concept in this entire chapter. It states that if two triangles are congruent, then each of their corresponding parts (angles and sides) are equal. This is a fundamental principle that underlies all our discussions on congruency. These rules help us determine whether two triangles are congruent or not. But remember, congruence is not just about size; it's also about shape! If two triangles have the same angles and sides, then they are congruent, regardless of their size. Rule states that two triangles are congruent if corresponding anglesand sides are equal. In the figure, AB=PQ, ∠A=∠P, and ∠B=∠Q, so ΔACB≅ΔPQR by ASA congruency. The AAS congruency rule states that two triangles are congruent when any two angles of a triangle and non-included side are equal to the corresponding angles and side of another triangle, satisfying the congruency. For the given figure, BC=QR,∠A=∠P, and ∠B=∠Q, so ΔACB≅ΔDFE by AAS congruency. The RHS congruency rule is applicable only to right-angled triangles. It states that if two sides (hypotenuse and one side) o","cbCaigqXHqkP00Dx","https://ap.wps.com/l/cbCaigqXHqkP00Dx","pdf",174642,"English","# Congruent Triangles\n## Meaning of Congruence (≅)\n## Congruence Rules: SSS, SAS, ASA, AAS\n## Right Triangles: RHS\n## CPCT (Corresponding Parts of Congruent Triangles)\n## Properties and Examples","[{\"question\":\"What does it mean when two triangles are congruent?\",\"answer\":\"Two triangles are congruent when they have the same shape and size, so one can be perfectly overlapped with the other. This requires equality of corresponding angles and sides.\"},{\"question\":\"What are the four main triangle congruence rules?\",\"answer\":\"The document lists SSS, SAS, ASA, and AAS. Each rule states specific sets of equal sides and angles that guarantee the triangles are congruent.\"},{\"question\":\"How does CPCT help in proving triangle congruence?\",\"answer\":\"CPCT states that if two triangles are congruent, then their corresponding parts—both angles and sides—are equal. It is the principle used to conclude equality after establishing congruence.\"}]","Congruent Triangles - Geometry Rules and Theorems | PDF",1790279002]