[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-573392-105":53,"doc-detail-573392-en":126},{"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":119,"head_meta":121,"extra_data":123,"updated_unix":125},105,"en","list-of-valid-reasons-for-proofs-geometry-postulates-and-theorems","List of Valid Reasons for Proofs - Geometry Postulates and Theorems","","Geometry reference list compiling valid reasons used for proofs, organized by foundational angle, segment, line, and transformation concepts. Covers key postulates and definitions including Angle Addition, Segment Addition, Angle bisector, midpoint, right angle, perpendicular, parallel, congruent, complementary and supplementary angles, with translations, rotations, and reflections. Includes core properties of equality and distributive relationships, angle pairs such as linear pairs and vertical angles, ruler and protractor postulates, arc and area/volume postulates, plus converse statements and triangle congruence and similarity criteria.",{"@graph":63,"@context":118},[64,80,101],{"@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":51,"@type":70,"position":76},"https://docshare.wps.com/template/general/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/list-of-valid-reasons-for-proofs-geometry-postulates-and-theorems/573392/",4,{"url":78,"name":59,"@type":81,"image":82,"author":87,"headline":59,"publisher":90,"fileFormat":93,"inLanguage":57,"description":61,"dateModified":94,"datePublished":95,"encodingFormat":93,"isAccessibleForFree":96,"interactionStatistic":97},"DigitalDocument",{"url":83,"@type":84,"width":85,"height":86},"https://docshare.wps.com/thumbnails/list-of-valid-reasons-for-proofs-geometry-postulates-and-theorems/573392.png","ImageObject",442,249,{"name":88,"@type":89},"Jake","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-10-17","2026-10-14",true,{"@type":98,"interactionType":99,"userInteractionCount":79},"InteractionCounter",{"@type":100},"ViewAction",{"@type":102,"mainEntity":103},"FAQPage",[104,110,114],{"name":105,"@type":106,"acceptedAnswer":107},"What are the main types of reasons included for geometry proofs in this list?","Question",{"text":108,"@type":109},"The list groups reasons by definitions, postulates, properties, transformations, converse statements, and triangle congruence/similarity criteria.","Answer",{"name":111,"@type":106,"acceptedAnswer":112},"Which angle-related definitions and postulates are explicitly listed?",{"text":113,"@type":109},"It includes angle bisector and angle addition postulate, as well as supplementary/complementary angles, adjacent angles, linear pairs, vertical angles, and corresponding/alternate angle postulates for parallels.",{"name":115,"@type":106,"acceptedAnswer":116},"What triangle congruence and similarity criteria are provided?",{"text":117,"@type":109},"It provides SSS, SAS, ASA, AAS, HL (for right triangles), CPCTC for congruence, and SSS similarity, SAS similarity, and AA similarity for similarity.","https://schema.org",{"og:url":78,"og:type":120,"og:title":59,"og:site_name":91,"og:description":61},"article",{"robots":122,"canonical":78},"index,follow",{"doc_id":124,"site_id":56},573392,1792012125,{"code":4,"msg":5,"data":127},{"doc_id":124,"user_id":128,"nickname":88,"user_avatar":129,"doc_module":9,"category_id":50,"category_name":51,"doc_title":59,"doc_description":61,"doc_content":130,"file_id":131,"file_url":132,"file_type":133,"file_size":134,"view_count":79,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":73,"language":135,"language_code":57,"site_id":56,"html_lang":57,"table_of_contents":136,"faqs":137,"seo_title":138,"seo_description":61,"update_tm":139,"read_time":9},962084928904,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","List of Valid Reasons for Proofs  \nImportant Definitions: Angle Addition Postulate  \nDefinition of Angle bisector  \nSegment Addition Postulate  \nDefinition of Segment bisector  \nTranslation  \nDefinition of Midpoint  \nRotation  \nDefinition of Right angle  \nReflection  \nDefinition of Perpendicular  \nParallel Postulate  \nDefinition of Congruent  \nPerpendicular Postulate  \nDefinition of Complementary angles  \nDefinition of Supplementary angles  \nDefinition of Adjacent Angles  \nDefinition of Parallel Lines  \nPostulates and Properties:  \nAddition Property  \nSubtraction property Multiplication property Division property  \nAddition Property of equality Subtraction property of equality Multiplication property of equality Division property of equality Distributive property Substitution property  \nTransitive property Symmetric property Reflexive property  \nVertical angles are congruent Linear pair Postulate  \nRuler Postulate  \nProtractor Postulate  \nTransitive Property of Parallel Lines Corresponding Angles Postulate Slope of Parallel Lines  \nSlope of Perpendicular Lines  \nArc Addition  \nArea of a Square Postulate Area Congruence Postulate  \nArea Addition Postulate  \nVolume of a Cube  \nVolume Congruence Postulate  \nVolume Addition Postulate  \n// Line Angle Relationships:  \n//, Alternate interior angles are congruent  \n//, Alternate exterior angles are congruent //, Corresponding angles are congruent (Postulate)//, Consecutive interior angles are supplementary  \nConverses:  \nCorresponding angles Converse Alternate Interior angles Converse  \nAlternate Exterior Converse  \nConsecutive interior Converse  \nTriangles Congruence/Similarity:  \nSSS  \nSAS  \nASA  \nAAS  \nHL (only right triangles)  \nCPCTC  \nSSS Similarity  \nSAS similarity AA similarity  \nTriangle Related Theorems:  \nTriangle sum theorem  \nBase angle theorem Converse Base angle Theorem Exterior angle theorem Third angles theorem  \nRight Angle Theorem  \nCongruent Supplement Angle Theorem  \nCongruent Complement Angle Theorem  \nAxioms:  \n5. Through any two points there exist exactly one line  \n6. A line contains at least two points.  \n7. If two lines intersect, then their intersection is exactly one point.  \n8. Through any three noncollinear points there exists exactly one plane.  \n9. A plane contains at least three noncollinear points.  \n10. If two points lie in a plane, then the line containing them lies in the plane.  \n11. If two planes intersect, then their intersection is a line.  \nEXTRAS…….","cbCaiuKrXdzVH910","https://ap.wps.com/l/cbCaiuKrXdzVH910","pdf",186926,"English","# Important Definitions\n## Angle bisector, Segment bisector, Midpoint\n## Transformations (Translation, Rotation, Reflection)\n# Postulates and Properties\n## Angle relationships and parallel lines\n## Equality, distributive, and substitution properties\n# Arc, Area, and Volume Postulates\n## Arc Addition; square area; cube volume\n# Line-Angle Relationships and Converses\n## Vertical angles, linear pairs, alternate/corresponding\n# Triangles Congruence/Similarity and Theorems\n## SSS, SAS, ASA, AAS, HL, CPCTC; similarity criteria\n# Axioms","[{\"question\":\"What are the main types of reasons included for geometry proofs in this list?\",\"answer\":\"The list groups reasons by definitions, postulates, properties, transformations, converse statements, and triangle congruence/similarity criteria.\"},{\"question\":\"Which angle-related definitions and postulates are explicitly listed?\",\"answer\":\"It includes angle bisector and angle addition postulate, as well as supplementary/complementary angles, adjacent angles, linear pairs, vertical angles, and corresponding/alternate angle postulates for parallels.\"},{\"question\":\"What triangle congruence and similarity criteria are provided?\",\"answer\":\"It provides SSS, SAS, ASA, AAS, HL (for right triangles), CPCTC for congruence, and SSS similarity, SAS similarity, and AA similarity for similarity.\"}]","List of Valid Reasons for Proofs - Geometry Postulates and Theorems | PDF",1791938840]