[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-386333-105":59,"doc-detail-386333-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","geom_ch_4_notes-triangles-angles-in-triangles-congruent-triangles","Geom_Ch_4_Notes - Triangles - Angles in Triangles - Congruent Triangles","","Geometry Chapter 4 notes on triangles focus on angle relationships and congruence reasoning. Students learn to determine missing interior angles using the Triangle Sum Theorem and to compute exterior angles using the Exterior Angle Theorem. The congruent triangles section introduces congruence statements, corresponding parts, and rigid transformations, then applies CPCTC. The document also starts SSS and SAS foundations for proving triangles congruent through structured two-column proofs.",{"@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/geom_ch_4_notes-triangles-angles-in-triangles-congruent-triangles/386333/",{"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/geom_ch_4_notes-triangles-angles-in-triangles-congruent-triangles/386333.png","ImageObject",300,407,{"name":92,"@type":93},"RuangKosong","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",13,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How do you find missing interior angles in a triangle?","Question",{"text":113,"@type":114},"Use the Triangle Sum Theorem, where the three interior angles of a triangle add up to 180°.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What does the Exterior Angle Theorem say about an exterior angle?",{"text":118,"@type":114},"An exterior angle of a triangle equals the sum of the two remote interior angles.",{"name":120,"@type":111,"acceptedAnswer":121},"What is CPCTC used for in congruent triangles?",{"text":122,"@type":114},"Given two triangles are congruent, CPCTC states that corresponding parts (angles and sides) are congruent, allowing missing measures to be found.","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},386333,1790377828,{"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":46,"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":31,"preview_page_count":4},962090883219,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","| Geometry Ch 4 Notes: Triangles\u003Cbr>4.1 Notes: Angles in Triangles\u003Cbr>Objectives:\u003Cbr>• Students will be able to find missing interior angles in triangles.\u003Cbr>• Students will be able to find exterior angles in triangles.\u003Cbr>Exploration \\#1: Use the following link to explore angles in a triangle:\u003Cbr>[https://www.geogebra.org/m/FzUM9TeD](https://www.geogebra.org/m/FzUM9TeD)\u003Cbr>• Click on the vertices of the triangle to change the angle measurements.\u003Cbr>• What do you notice?\u003Cbr>• Make a conjecture (“guess”) about the angles in a triangle.\u003Cbr>Triangle Sum Theorem The sum of the measures of the interior angles of a triangle is  .\u003Cbr>∠􀡭 + ∠􀡮 + ∠􀡯 =   ° \u003Cbr>A good animation of the Triangle Sum Theorem: [https://www.geogebra.org/m/FAhtKpR5](https://www.geogebra.org/m/FAhtKpR5)\u003Cbr>Examples 1 – 4: Find the measure of each missing angle in the triangle shown. |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- |\n| 1) | |  | 2) You try! | |  |\n| 3) You try! |  | | 4) You try! |  | |\n| [washoeschools.net/DRHSmath](washoeschools.net/DRHSmath) 1 |  |  |  |  |  |\n\n\n| Geometry Ch 4 Notes: Triangles\u003Cbr>Examples 5 – 7: Find the measure of the variable. |  |\n| --- | --- |\n| 7) You Try! | |\n| 8) Find the measure of ∠􀜥 in the triangle from \\#7 . |  |\n| Some new names for special angles in a triangle:\u003Cbr>[washoeschools.net/DRHSmath](washoeschools.net/DRHSmath) 2\u003Cbr>|  |\n\nGeometry Ch 4 Notes: Triangles  \nExploration \\#2: [https://www.geogebra.org/m/sA5Mb4vd](https://www.geogebra.org/m/sA5Mb4vd)  \n• Click on the link to explore the relationship between an Exterior Angle and its two Remote Interior Angles.  \n• Make a conjecture:  \nEXTERIOR ANGLE THEOREM  \n\n| Exterior Angle Theorem | The measure of an exterior angle of a triangle is equal to the   of the two remote interior angles. | |\n| --- | --- | --- |\n\nWhy is this true?  \nExample \\#9: Find the measure of each exterior angle (∠1) .  \na. b. YOU TRY!!  \nExample \\#10: Find the value of 􀝔 in each triangle.  \na.  \nb. YOU TRY!!  \n[washoeschools.net/DRHSmath](washoeschools.net/DRHSmath) 3  \nGeometry Ch 4 Notes: Triangles  \n4.2 Notes: Intro to Congruent Triangles  \nObjectives:  \n• Students will be able to make a congruency statement for congruent triangles.  \n• Students will be able to list corresponding parts for congruent triangles.  \n• Students will be able to find missing measures in congruent triangles.  \n\n| Congruent Triangles | If two triangles are congruent, then there is a   transformation (or more than one) that   one shape onto the other. | |\n| --- | --- | --- |\n| Congruence Statement | A congruence statement lists two   shapes. The order of the letters listed shows which corresponding parts are congruent. | |\n| CPCTC | Given that two triangles are congruent, then C P  of C T  are C  |  |\n\nExample \\#1:  \nGiven that ∆􀜣􀜤􀜥 ≅ ∆􀜨􀜧􀜦 . Identify all corresponding sides and corresponding angles. a. ̅̅􀜣̅̅􀜤 ≅ _______ d. ∠􀜣 ≅ __________  \nb. ̅̅􀜤̅̅􀜥 ≅ _______ e. ∠􀜤 ≅ __________  \nc. ̅̅􀜣̅̅􀜥 ≅ _______ f. ∠􀜥 ≅ __________  \n[washoeschools.net/DRHSmath](washoeschools.net/DRHSmath) 4  \nGeometry Ch 4 Notes: Triangles  \nExample \\#2:  \nComplete the congruence statement for the pair of triangles shown.  \nCongruence Statement: ∆􀜳􀜴􀜲 ≅    \nYOU TRY! Example \\#3:  \nComplete the congruence statement for the pair of triangles shown.  \nThen identify all corresponding sides and angles.  \nCongruence Statement:  \na. ̅̅̅􀜹̅̅􀜺 ≅   d. ∠􀜺 ≅    \nb. ̅̅̅􀜹̅̅􀜻 ≅   f. ∠􀜻 ≅    \nc. ̅̅􀜺̅̅􀜻 ≅   g. ∠􀜹 ≅    \nYOU TRY! Example \\#4: Given the corresponding parts that are congruent for two triangles, write the congruence statement for the two triangles.  \n̅̅̅̅􀜲􀜮 ≅ ̅̅􀜣̅̅􀜤  \n̅̅̅̅􀜮􀜸 ≅ ̅̅􀜤̅̅􀜥  \n∠􀜲 ≅ ∠􀜣  \n∠􀜮 ≅ ∠􀜤  \n̅̅􀜸̅̅􀜲 ≅ ̅̅􀜥̅̅􀜣∠􀜸 ≅ ∠􀜥  \nCongruence Statement:  \nExample \\#5:  \nIn the diagram, ∆􀜦􀜱􀜩 ≅ ∆􀜥􀜣􀜶 .  \na. Find the value of 􀝔 .  \nb. Find the value of 􀝕 .  \nc. Find the perimeter of ∆􀜥􀜣􀜶 .  \n[washoeschools.net/DRHSmath](washoeschools.net/DRHSmath)  \n5  \n\n| Geometry Ch 4 Notes: Triangles |  |  |\n| --- | --- | --- |\n| YOU TRY! Example \\#6:\u003Cbr>In the diag","cbCaihHuvxaLpCV8","https://ap.wps.com/l/cbCaihHuvxaLpCV8","pdf",1495424,"English","# 4.1 Notes: Angles in Triangles\n## Objectives\n## Exploration #1: Triangle angle relationships\n## Triangle Sum Theorem\n## Examples and “You Try”\n# 4.2 Notes: Intro to Congruent Triangles\n## Objectives\n## Congruence statements and corresponding parts\n## CPCTC\n## Examples and “You Try”\n# 4.3 Notes: SSS and SAS\n## Objectives\n## Exploration #1: Side length comparison\n## SSS postulate","[{\"question\":\"How do you find missing interior angles in a triangle?\",\"answer\":\"Use the Triangle Sum Theorem, where the three interior angles of a triangle add up to 180°.\"},{\"question\":\"What does the Exterior Angle Theorem say about an exterior angle?\",\"answer\":\"An exterior angle of a triangle equals the sum of the two remote interior angles.\"},{\"question\":\"What is CPCTC used for in congruent triangles?\",\"answer\":\"Given two triangles are congruent, CPCTC states that corresponding parts (angles and sides) are congruent, allowing missing measures to be found.\"}]","Geom_Ch_4_Notes - Triangles - Angles in Triangles - Congruent Triangles | PDF",1790273342]