[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-573390-105":53,"doc-detail-573390-en":120},{"code":4,"msg":5,"data":6},0,"success",[7,14,19,24,29,34,39,44,49],{"id":8,"doc_module":9,"doc_module_name":10,"category_name":11,"show_sort_weight":12,"slug":13},11,1,"Template","Presentations",90,"presentations",{"id":15,"doc_module":9,"doc_module_name":10,"category_name":16,"show_sort_weight":17,"slug":18},12,"Resumes",80,"resumes",{"id":20,"doc_module":9,"doc_module_name":10,"category_name":21,"show_sort_weight":22,"slug":23},14,"Invoices",70,"invoices",{"id":25,"doc_module":9,"doc_module_name":10,"category_name":26,"show_sort_weight":27,"slug":28},15,"Posters",60,"posters",{"id":30,"doc_module":9,"doc_module_name":10,"category_name":31,"show_sort_weight":32,"slug":33},16,"Social Media",50,"social-media",{"id":35,"doc_module":9,"doc_module_name":10,"category_name":36,"show_sort_weight":37,"slug":38},17,"Forms",40,"forms",{"id":40,"doc_module":9,"doc_module_name":10,"category_name":41,"show_sort_weight":42,"slug":43},18,"Letters",30,"letters",{"id":45,"doc_module":9,"doc_module_name":10,"category_name":46,"show_sort_weight":47,"slug":48},21,"Paper Templates",5,"papers-templates",{"id":50,"doc_module":9,"doc_module_name":10,"category_name":51,"show_sort_weight":4,"slug":52},158,"General","general-158",{"code":4,"msg":54,"data":55},"ok",{"site_id":56,"language":57,"slug":58,"title":59,"keywords":60,"description":61,"schema_data":62,"social_meta":113,"head_meta":115,"extra_data":117,"updated_unix":119},105,"en","classifying-triangles-chapter-5-summary-sheet","Classifying Triangles - Chapter 5 Summary Sheet","","Chapter 5 Summary Sheet focused on classifying triangles by sides and angles, including equilateral, isosceles, scalene, equiangular, right, acute, and obtuse categories. Covers key angle relationships such as the triangle sum theorem (angles totaling 180°) and the exterior angle theorem. Includes criteria for congruent triangles, CPCTC (corresponding parts of congruent triangles are congruent), and outlines multiple shortcuts for proving congruence, with emphasis on proof statements and reasons.",{"@graph":63,"@context":112},[64,80,95],{"@type":65,"itemListElement":66},"BreadcrumbList",[67,71,74,77],{"item":68,"name":69,"@type":70,"position":9},"https://docshare.wps.com","Home","ListItem",{"item":72,"name":10,"@type":70,"position":73},"https://docshare.wps.com/template/",2,{"item":75,"name":16,"@type":70,"position":76},"https://docshare.wps.com/template/resumes/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/classifying-triangles-chapter-5-summary-sheet/573390/",4,{"url":78,"name":59,"@type":81,"author":82,"headline":59,"publisher":85,"fileFormat":88,"inLanguage":57,"description":61,"dateModified":89,"datePublished":89,"encodingFormat":88,"isAccessibleForFree":90,"interactionStatistic":91},"DigitalDocument",{"name":83,"@type":84},"\tJames","Person",{"url":68,"name":86,"@type":87},"DocShare","Organization","application/pdf","2026-10-14",true,{"@type":92,"interactionType":93,"userInteractionCount":4},"InteractionCounter",{"@type":94},"ViewAction",{"@type":96,"mainEntity":97},"FAQPage",[98,104,108],{"name":99,"@type":100,"acceptedAnswer":101},"How are triangles classified by sides, and what defines each type?","Question",{"text":102,"@type":103},"Equilateral triangles have all sides congruent. Isosceles triangles have exactly two congruent sides, and scalene triangles have no congruent sides.","Answer",{"name":105,"@type":100,"acceptedAnswer":106},"How does the triangle sum theorem relate the three interior angles?",{"text":107,"@type":103},"The sum of all interior angles of a triangle is 180°, expressed as m∠A + m∠B + m∠C = 180°.",{"name":109,"@type":100,"acceptedAnswer":110},"When is CPCTC used in a congruence proof?",{"text":111,"@type":103},"CPCTC is used only after two triangles have already been proven congruent, because it justifies that their corresponding parts are congruent.","https://schema.org",{"og:url":78,"og:type":114,"og:title":59,"og:site_name":86,"og:description":61},"article",{"robots":116,"canonical":78},"index,follow",{"doc_id":118,"site_id":56},573390,1791938831,{"code":4,"msg":5,"data":121},{"doc_id":118,"user_id":122,"nickname":83,"user_avatar":123,"doc_module":9,"category_id":15,"category_name":16,"doc_title":59,"doc_description":61,"doc_content":124,"file_id":125,"file_url":126,"file_type":127,"file_size":128,"view_count":4,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":73,"language":129,"language_code":57,"site_id":56,"html_lang":57,"table_of_contents":130,"faqs":131,"seo_title":132,"seo_description":61,"update_tm":119,"read_time":9},2336474466412,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","Classifying Triangles by Sides Equilateral  \nAll sides are ≅  \nChapter 5 Summary Sheet  \nIsosceles  \nVertex leg leg  \n angle  \nBase  \n angles  \nbase 2 sides are ≅  \nALWAYS KEEP!!!   \nScalene  \nNo sides are ≅  \nClassifying Triangles by Angles  \nEquiangular Right Acute Obtuse  \nleg  \nleg  \nAll angles are ≅ One right angle All angles are  \nless than 90°  \nOne angle is greater than 90°  \nTriangle Sum Theorem  \nB  \nThe sum of all the angle of a triangle is 180° . m∠A + m∠B + m∠C = 180°  \nA ~~ ~~ C  \nExterior Angle Theorem  \nThe measure of an exterior angle of a triangle is equal to  \nthe sum of the measures of the two non-adjacent interior angles.  \n1) If a triangle is isosceles, then its base angles are congruent.  \n2) If two angles of a triangle are congruent, then the sides opposite of the congruent angles are congruent.  \nm∠1 = m∠A + m∠B  \n1) If a triangle is equilateral, then it is also equiangular.  \n2) If a triangle is equiangular, then it is also equilateral. Note: All angles of an equiangular triangle measure 60° .  \nCongruent Triangles – Two triangles are congruent if all their corresponding angles and sides are congruent.  \nIn other words, the triangles are identical and can perfectly overlap.  \nEx:  \n∆ABC ≅ ∆DEF  \nAB ≅ DE  \n∠A ≅ ∠D  \nBC ≅ EF ∠B ≅ ∠E  \nE  \nF D  \nAC ≅ DF ∠C ≅ ∠F  \nCorresponding-parts that have the same structure.  \nNote: The corresponding used for triangles has a different meaning then the corresponding used for parallel lines and a transversal.  \nThe 5 Shortcuts for Proving Two Triangles are Congruent  \n\n| \u003Cbr>(Right ∆’s only) |  |  |\n| --- | --- | --- |\n| Included means that the angle is between the two congruent sides. | Included means that the side is between the two congruent angles. | There is an ASS shortcut, but it only works for right triangles and it is called HL. |\n\nStatements and Reasons for Proofs  \n\n| You know… | Statement |  | Reason |\n| --- | --- | --- | --- |\n| ∆ABC ≅ ∆DEF | AB ≅ DE or\u003Cbr>∠A ≅ ∠D | ( | CPCTC\u003Cbr>Corresponding Parts of Congruent Triangles are Congruent ) |\n\nImportant: The only time you will use CPCTC as a reason in a proof is after you have proven two triangles are congruent. It justifies that the corresponding parts of two triangles are congruent.","cbCaiid0NPbjbbzq","https://ap.wps.com/l/cbCaiid0NPbjbbzq","pdf",65536,"English","# Classifying Triangles by Sides\n## Equilateral\n## Isosceles\n## Scalene\n# Classifying Triangles by Angles\n## Equiangular\n## Right, Acute, Obtuse\n# Triangle Angle Theorems\n## Triangle Sum Theorem\n## Exterior Angle Theorem\n# Congruuent Triangles and Proof Shortcuts\n## CPCTC\n## Statements and Reasons","[{\"question\":\"How are triangles classified by sides, and what defines each type?\",\"answer\":\"Equilateral triangles have all sides congruent. Isosceles triangles have exactly two congruent sides, and scalene triangles have no congruent sides.\"},{\"question\":\"How does the triangle sum theorem relate the three interior angles?\",\"answer\":\"The sum of all interior angles of a triangle is 180°, expressed as m∠A + m∠B + m∠C = 180°.\"},{\"question\":\"When is CPCTC used in a congruence proof?\",\"answer\":\"CPCTC is used only after two triangles have already been proven congruent, because it justifies that their corresponding parts are congruent.\"}]","Classifying Triangles - Chapter 5 Summary Sheet | PDF"]