[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-571801-105":53,"doc-detail-571801-en":127},{"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":120,"head_meta":122,"extra_data":124,"updated_unix":126},105,"en","geometry-cheat-sheet","Geometry - Cheat Sheet","","Geometry cheat sheet compiling core formulas and relationships for lines, angles, triangles, quadrilaterals, circles, probability, and common transformations. Includes notation, equation and point-slope forms, parallel/perpendicular line rules, distance and midpoint formulas, and triangle congruence/similarity criteria (CPCTC and proportional sides). Covers parallelogram and trapezoid properties, coordinate transformations, perimeter/area/volume formulas for standard shapes, and circle angle theorems (tangent-radius right angles, inscribed-angle and arc-based congruence).",{"@graph":63,"@context":119},[64,80,102],{"@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":11,"@type":70,"position":76},"https://docshare.wps.com/template/presentations/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/geometry-cheat-sheet/571801/",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/geometry-cheat-sheet/571801.png","ImageObject",442,249,{"name":88,"@type":89},"Rainbow Cat","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-10-22","2026-10-13",true,{"@type":98,"interactionType":99,"userInteractionCount":101},"InteractionCounter",{"@type":100},"ViewAction",6,{"@type":103,"mainEntity":104},"FAQPage",[105,111,115],{"name":106,"@type":107,"acceptedAnswer":108},"What are the key formulas for lines in the cheat sheet?","Question",{"text":109,"@type":110},"The sheet provides the equation of a line and point-slope form, along with rules for handling parallel and perpendicular lines (including the negative reciprocal relationship).","Answer",{"name":112,"@type":107,"acceptedAnswer":113},"How does the cheat sheet define triangle congruence and similarity?",{"text":114,"@type":110},"It lists congruence methods such as SAS, SSS, AAS, HL (right triangles only), and ASA, and instructs using CPCTC when proven. For similarity, it includes AA and other listed criteria and notes that corresponding sides of similar triangles are proportional.",{"name":116,"@type":107,"acceptedAnswer":117},"Which circle angle theorems are included?",{"text":118,"@type":110},"It includes the tangent-radius right-angle rule, semicircle inscribed-angle right angles, congruence of inscribed angles intercepting the same arc, and angle relationships involving secants, tangents, and chords.","https://schema.org",{"og:url":78,"og:type":121,"og:title":59,"og:site_name":91,"og:description":61},"article",{"robots":123,"canonical":78},"index,follow",{"doc_id":125,"site_id":56},571801,1792016892,{"code":4,"msg":5,"data":128},{"doc_id":125,"user_id":129,"nickname":88,"user_avatar":130,"doc_module":9,"category_id":8,"category_name":11,"doc_title":59,"doc_description":61,"doc_content":131,"file_id":132,"file_url":133,"file_type":134,"file_size":135,"view_count":101,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":136,"language":137,"language_code":57,"site_id":56,"html_lang":57,"table_of_contents":138,"faqs":139,"seo_title":140,"seo_description":61,"update_tm":141,"read_time":76},962090769181,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","Geometry Cheat Sheet  \nNotation:  \n≅ congruent~ similar ∆ triangle ∢ angle ∥ parallel ⊥ perpendicular 22􀀰22􀀱 line segment AB ͡􀀰􀀱 arc AB  \nEquation of a Line:  \n􀁁 = 􀁂􀀸 + 􀁄  \n􀁂 = 􀀴􀁅􀀼􀁆􀀵 =  \n∆􀁁  􀁇􀀽􀀴􀀵∆􀀸 = 􀁇􀁈􀀾  \n􀁄 = 􀁁 − 􀀽􀀾􀀿􀀵􀁇􀀶􀀵􀁆􀀿  \nPoint Slope Form:  \n􀁁 − 􀁁! = 􀁂 (􀀸 − 􀀸!)  \nParallel and Perpendicular Lines:  \n􀁊􀁀􀁇􀁀􀁅􀁅􀀵􀁅 : Same Slope 􀁂 = 􀁂  \nPerpendicular: Take negative reciprocal  \n􀁂 → − 1L􀁂  \nDistance Formula:  \n􀁍 = N(􀀸\" − 􀀸! )\" + (􀁁\" − 􀁁! )\"  \nMidpoint Formula:  \n􀁏 = (􀀸\"~~ ~~+~~2 ~~􀀸! , 􀁁\"~~ ~~+~~2 ~~􀁁!~~ ~~)  \nLaw of Sins:  \n 􀁀   􀁄   􀀶 􀁒􀀽􀀾 􀀰 = 􀁒􀀽􀀾 􀀱 = 􀁒􀀽􀀾 􀁓  \nLaw of Cosines:  \n􀀶 \" = 􀁀 \" + 􀁄 \" − 2􀁀􀁄􀀶􀀼􀀴􀁓  \nConverting Degrees to Radians:  \n􀀵􀀸 : 60° × ~~ 1~~~~0~~ =   \nConverting Radians to Degrees:  \n􀀵􀀸 :  × ~~ ~~10 = 60°  \nAngle of Elevation:  \n􀀪 􀀧 􀀱􀀲 ℎ􀀩  \nSOH CAH TOA:  \n􀀢􀀣􀀤􀀥􀀦􀀧􀀨􀀩  \n􀀰􀀬􀀬􀀭􀀯􀀱􀀩􀀧  \n􀀴􀀽􀀾 (􀀸) =􀀶􀀼􀀴 (􀀸 ) =  \n􀀼􀁆􀁆􀀼􀀴􀀽􀀿􀀵  \nℎ􀁁􀁆􀀼􀀿􀀵􀀾􀁈􀀴􀀵  􀁀􀁍􀁕􀁀􀀶􀀵􀀾􀀿 ℎ􀁁􀁆􀀿􀀵􀀾􀁈􀀴􀀵  \n􀀿􀁀􀀾 (􀀸 ) =  \n 􀀼􀁆􀁆􀀼􀀴􀀽􀀿􀀵 􀁀􀁍􀁕􀁀􀀶􀀵􀀾􀀿  \n\n| Inverse Trig. Functions:\u003Cbr>􀀴􀀵􀀶 (􀀸) = 􀀶􀀼~~ ~~􀀴1~~(~~􀀸~~ )~~\u003Cbr>􀀶􀀴􀀶 (􀀸 ) = 1~~􀀴􀀽􀀾(~~􀀸~~ ) ~~ 1 \u003Cbr>􀀶􀀼􀀿 (􀀸) =􀀿􀁀􀀾 (􀀸 ) | Complimentary Angles: |  |\n| --- | --- | --- |\n|  | 􀀴􀀽􀀾 (90° − 􀁟) = 􀀶􀀼􀀴 (􀁟) 􀀶􀀴􀀶 (90° − 􀁟) = | 􀀴􀀵􀀶 (􀁟) |\n|  | 􀀶􀀼􀀴 (90° − 􀁟) = 􀀴􀀽􀀾 (􀁟) 􀀴􀀵􀀶 (90° − 􀁟) = | 􀀶􀀴􀀶 (􀁟) |\n|  | 􀀿􀁀􀀾 (90° − 􀁟) = 􀀶􀀼􀀿 (􀁟) 􀀶􀀼􀀿 (90° − 􀁟) = | 􀀿􀁀􀀾 (􀁟) |\n\n©MathSux. All rights reserved.  \n1  \nProbability:  \nn=Total number of objects r=Number of chosen objects  \nPermutation:  \n(Order matters)  \nCombinations  \n(Order doesn’t matter)  \nConditional: 􀁊 (􀀱|􀀰) = %(%'(*))  \nAnd:  \n􀁊 (􀀰 ∩ 􀀱) = 􀁊 (􀀰) × 􀁊 (􀀱) (Independent)  \n􀁊 (􀀰 ∩ 􀀱) = 􀁊 (􀀰) × (􀀱|􀀰) (Dependent)  \nOr:  \n􀁊 (􀀰 ∪ 􀀱) = 􀁊 (􀀰) + 􀁊 (􀀱) − 􀁊 (􀀰 ∩ 􀀱) (Not Mutually Exclusive)  \n􀁊 (􀀰 ∪ 􀀱) = 􀁊 (􀀰) + 􀁊 (􀀱) (Mutually Exclusive)  \nTransversals: Given two lines are parallel and are cut by a transversal line.  \nAlternate Interior Angles:  \n∢􀀶 = ∢􀁡 􀁀􀀾􀁍 ∢􀁍 = ∢􀀵  \nAlternate Exterior Angles:  \n∢􀁀 = ∢ℎ 􀁀􀀾􀁍 ∢􀁄 = ∢􀁢  \nCorresponding Angles:  \n∢􀁀 = ∢􀀵 , ∢􀁄 = ∢􀁡, ∢􀀶 = ∢􀁢 , 􀁀􀀾􀁍 ∢􀁍 = ∢ℎ  \nSupplementary Angles:  \n∢􀀶 + ∢􀀵 = 180°, ∢􀁍 + ∢􀁡 = 180°, ∢􀁀 + ∢􀁄 = 180°,  \n∢􀀶 + ∢􀁍 = 180°, ∢􀀵 + ∢􀁡 = 180° , ∢􀁢 + ∢ℎ = 180°  \nProperties of a Parallelogram:  \n1) Opposite sides are parallel.  \n2) Pairs of opposite sides are congruent.  \n3) Pairs of opposite angles are congruent.  \n4) Diagonals bisect each other.  \n5) Diagonals separate parallelogram into 2 congruent triangles.  \n6) Interior angles add up to 360° .  \nThe following shapes are all Parallelograms:  \n1) Square (also a rhombus and a rectangle)  \n2) Rhombus   \n3) Rectangle   \nTransformations:  \nReflection in the x-axis: 􀀰 (􀀸, 􀁁) → 􀀰 $ (􀀸, −􀁁)  \nReflection in the y-axis: 􀀰 (􀀸, 􀁁) → 􀀰 $ (−􀀸, 􀁁)  \nReflection over the line y=x: 􀀰 (􀀸, 􀁁) → 􀀰 $ (􀁁, 􀀸 )  \nReflection through the origin: 􀀰 (􀀸, 􀁁) → 􀀰 $ (−􀀸, −􀁁)  \nRotation of 90° : 􀀰 (􀀸, 􀁁) → 􀀰 $ (−􀁁, 􀀸 )  \nRotation of 180° : 􀀰 (􀀸, 􀁁) → 􀀰 $ (−􀀸, −􀁁)  \nRotation of 270° : 􀀰 (􀀸, 􀁁) → 􀀰 $ (􀁁, −􀀸)  \nDilation of n: 􀀰 (􀀸, 􀁁) → 􀀰 $ (􀀸􀀾, 􀁁􀀾)  \nTransformation to the left m units and up n units: 􀀰 (􀀸, 􀁁) → 􀀰 $ (􀀸 − 􀁂, 􀁁 + 􀀾)  \n©MathSux. All rights reserved.  \n2  \nCongruent Triangles ≅: SAS  \nSSS  \nAAS  \nHL –(only for right triangles) ASA  \nWhen proven use: Corresponding parts of congruent triangles are congruent (CPCTC)  \nSimilar Triangles ~ :  \nAA SSS SAS  \nWhen proven use: Corresponding sides of similar triangles are in proportion.  \n\n| Midpoint Triangles Theorem:\u003Cbr>∆􀀰􀀱􀁓 has midpoints at point D and point E. When points D and E are connected, the length of 22􀁧22􀁨 is half the length of base 22􀀱22􀁓 .\u003Cbr>􀀢\u003Cbr>􀀸  􀀸  􀀹\u003Cbr>􀀺  2􀀸  􀀻\u003Cbr>|  | Medians of a Trapezoid:\u003Cbr>In a trapezoid, the length of median z is equal to half the length of the sum of both bases 􀀸 and 􀁁 .\u003Cbr>1\u003Cbr>􀁪 = (􀀸 + 􀁁) 2\u003Cbr>􀀸\u003Cbr>􀁪\u003Cbr>􀁁\u003Cbr>|  |\n| --- | --- | --- | --- |\n| Types of Triangles:\u003Cbr>Scalene: No sides are equal.\u003Cbr>Equilateral: All sides are equal.\u003Cbr>Isosceles: Two sides are equal.\u003Cbr>Acute: All angles are \u003C 90° .\u003Cbr>Obtuse: There is an angle > 90° .\u003Cbr>Right: There is an angle = 90° . External Angle Triangles Theorem:\u003Cbr>When any side of a triangle is extended the value of its angle is suppleme","cbCaioE4nX3hz8gm","https://ap.wps.com/l/cbCaioE4nX3hz8gm","pdf",1113913,7,"English","# Notation and Line Equations\n## Equation of a Line and Point Slope Form\n# Angles and Line Relationships\n## Parallel and Perpendicular Lines\n# Trigonometry and Angle Conversions\n## Degrees to Radians and SOH CAH TOA\n# Inverse Trigonometric Functions and Complementary Angles\n# Triangle Concepts\n## Congruent Triangles Criteria (SAS, SSS, AAS, HL, ASA)\n## Similar Triangles Criteria (AA, SSS, SAS)\n# Parallelograms and Trapezoids\n## Parallelogram Properties\n## Medians of a Trapezoid\n# Transformations\n## Reflections, Rotations, and Dilations\n# Area, Perimeter, and Volume\n## Common Shape Formulas\n# Polygons and Trigonometric Angle Sums\n# Circles and Circle Theorems\n## Parts of a Circle and Angle Theorems","[{\"question\":\"What are the key formulas for lines in the cheat sheet?\",\"answer\":\"The sheet provides the equation of a line and point-slope form, along with rules for handling parallel and perpendicular lines (including the negative reciprocal relationship).\"},{\"question\":\"How does the cheat sheet define triangle congruence and similarity?\",\"answer\":\"It lists congruence methods such as SAS, SSS, AAS, HL (right triangles only), and ASA, and instructs using CPCTC when proven. For similarity, it includes AA and other listed criteria and notes that corresponding sides of similar triangles are proportional.\"},{\"question\":\"Which circle angle theorems are included?\",\"answer\":\"It includes the tangent-radius right-angle rule, semicircle inscribed-angle right angles, congruence of inscribed angles intercepting the same arc, and angle relationships involving secants, tangents, and chords.\"}]","Geometry - Cheat Sheet | PDF",1791923775]