[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-571806-105":3,"detail-sidebar-cat-1-en-105":85,"doc-detail-571806-en":131},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":78,"head_meta":80,"extra_data":82,"updated_unix":84},105,"en","geometry-cheat-sheet-chapter-1-key-concepts-and-constructions","Geometry Cheat Sheet - Chapter 1 - Key Concepts and Constructions","","Geometry cheat sheet covering fundamental angle relationships, conditional statement vocabulary, reasoning types, and key theorem notes. Includes postulates such as segment addition and angle addition, definitions of adjacent, vertical, complementary, supplementary, and linear pairs, plus the angle bisector concept. Provides step-by-step constructions for congruent segments and angles, constructing a perpendicular bisector, and building an angle bisector. Also summarizes inductive reasoning, counterexamples, conditional forms, and logical laws (detachment and syllogism) with theorem-style proof structure.",{"@graph":14,"@context":77},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/template/","Template",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/template/general/","General",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/template/geometry-cheat-sheet-chapter-1-key-concepts-and-constructions/571806/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/geometry-cheat-sheet-chapter-1-key-concepts-and-constructions/571806.png","ImageObject",442,249,{"name":42,"@type":43},"SANS","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-22","2026-10-13",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",9,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69,73],{"name":60,"@type":61,"acceptedAnswer":62},"What is the Segment Addition Postulate and how is it used?","Question",{"text":63,"@type":64},"If points A, B, and C are collinear and B is between A and C, then AB + BC = AC. It helps relate segment lengths along a line.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How do you construct congruent segments and congruent angles?",{"text":68,"@type":64},"For congruent segments, draw a ray with endpoint C, set the compass to AB, transfer the length to point C, and mark the intersection point. For congruent angles, draw an arc from vertex A to mark intersections, then transfer the corresponding arc length to the new ray and connect the needed points.",{"name":70,"@type":61,"acceptedAnswer":71},"What are the converse, inverse, and contrapositive of a conditional statement?",{"text":72,"@type":64},"For a conditional p → q, the converse swaps hypothesis and conclusion (q → p), the inverse negates both (if not p then not q), and the contrapositive negates both with roles reversed (if not q then not p).",{"name":74,"@type":61,"acceptedAnswer":75},"How do deductive reasoning tools like the Law of Detachment and Law of Syllogism work?",{"text":76,"@type":64},"The Law of Detachment states that if p → q is true and p is true, then q is true. The Law of Syllogism states that if p → q is true and q → r is true, then p → r is true.","https://schema.org",{"og:url":32,"og:type":79,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":81,"canonical":32},"index,follow",{"doc_id":83,"site_id":7},571806,1792009592,{"code":4,"msg":86,"data":87},"success",[88,93,98,103,108,113,118,123,128],{"id":89,"doc_module":22,"doc_module_name":25,"category_name":90,"show_sort_weight":91,"slug":92},11,"Presentations",90,"presentations",{"id":94,"doc_module":22,"doc_module_name":25,"category_name":95,"show_sort_weight":96,"slug":97},12,"Resumes",80,"resumes",{"id":99,"doc_module":22,"doc_module_name":25,"category_name":100,"show_sort_weight":101,"slug":102},14,"Invoices",70,"invoices",{"id":104,"doc_module":22,"doc_module_name":25,"category_name":105,"show_sort_weight":106,"slug":107},15,"Posters",60,"posters",{"id":109,"doc_module":22,"doc_module_name":25,"category_name":110,"show_sort_weight":111,"slug":112},16,"Social Media",50,"social-media",{"id":114,"doc_module":22,"doc_module_name":25,"category_name":115,"show_sort_weight":116,"slug":117},17,"Forms",40,"forms",{"id":119,"doc_module":22,"doc_module_name":25,"category_name":120,"show_sort_weight":121,"slug":122},18,"Letters",30,"letters",{"id":124,"doc_module":22,"doc_module_name":25,"category_name":125,"show_sort_weight":126,"slug":127},21,"Paper Templates",5,"papers-templates",{"id":129,"doc_module":22,"doc_module_name":25,"category_name":29,"show_sort_weight":4,"slug":130},158,"general-158",{"code":4,"msg":86,"data":132},{"doc_id":83,"user_id":133,"nickname":42,"user_avatar":134,"doc_module":22,"category_id":129,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":140,"language":141,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":12,"update_tm":145,"read_time":146},962090760505,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","# Geometry Cheat SheetChapter 1\n\n■ Postulate 1-6  \nSegment Addition Postulate-If three points A,B,and C are collinear and B is between Aand C,then AB+BC=AC.  \n■ Postulate 1-7  \nAngle Addition Postulate -If point B is in the interior of AOC,thenm AOB+m BOC=m AOC.  \n■ Adjacent Angles-two coplanar angles with a common side,a common vertex,and nocommon interior points.  \n■ Vertical Angles-two angles whose sides are opposite rays.  \n■ Complementary Angles -two angles whose measures have a sum of 90.Each angle iscalled the complement of the other.  \n■ Supplementary Angles-two angles whose measures have a sum of 180.Each angle iscalled the supplement of the other.  \n■ Postulate 1-9 Linear Pair Postulates-If two angles form a linear pair,then they aresupplementary.  \n■Angle Bisector-a ray that divides an angle into two congruent angles.Its endpoint is atthe angle vertex within the ray,a segment with the same endpoint is also an anglebisector.  \n## Constructions\n\n### ■ Constructing Congruent Segments-\n\n■ Step One:Draw a ray with endpoint C.  \n■ Step Two:Open the compass to the length of AB.  \n■ Step Three:With the same compass setting,put the compass point on point C.Draw anarc that intersects the ray.Label the point of intersection D.  \n### ■ Constructing Congruent Angles-\n\n■ Step One:Draw a ray with endpoint S.  \n■ Step Two:With the compass on vertex A,draw an arc that intersects the sides of A.Label the points of intersection B and C.  \n■ Step Three:With the same compass setting,put the compass point on point S.Draw anarc and label its point of intersection with the ray as R.  \n■ Step Four:Open the compass to the length BC.Keeping the same compass setting,putthe compass point on R.Draw an arc to locate point T.  \n■ Step Five:Draw ST  \n### ■ Constructing the Perpendicular Bisector-\n\n■ Step One:Put the compass on point A and draw a long arc.Be sure the opening isgreater than Y AB.  \n■ Step Two:With the same compass setting,put the compass point on point B and drawanother long arc.Label the points where the two arcs intersect as X and Y.  \n■ Step Three:Draw XY.Label the point of intersection of AB and XY as M,the midpoint ofAB.  \n2-1  \n■ Constructing the Angle Bisector-  \n■ Step One:Put the compass point on vertex A.Draw an arc that intersects the sides of  \nA.Label the points of intersection B and C.  \n■ Step Two:Put the compass on point Cand draw an arc.With the same compasssetting,draw an arc using point B.Be sure the arcs intersect.Label the point where thetwo arcs intersect at D.  \n■ Step Three:Draw AD.  \n## Inductive reasoning\n\nInductive reasoning is a type of reasoning that reachesconclusions based on a pattern of specific examples orpast events.  \nExampleYou see four people walk into a building.Each person emerges with a small bagcontaining food.You use inductivereasoning to conclude that this buildingcontains a restaurant.  \n## Counterexample\n\nAn example showing that a statement is false.  \nExample Statement All apples are red.  \nCounterexample A Granny Smith apple is green.  \n◎ A conditional is an if-then statement  \n>p→q Read as \"if p thenq\"or“p implies q”  \n>Hypothesisfollows“if\",part\"p”  \n>Conclusionfollows“then”,part“q”  \nakE hot  \n\n| Key Concept Related Conditional Statements   |  |  |  |  |\n| --- | --- | --- | --- | --- |\n| Statement   | How to  \u003Cbr>Write It   | Example   | Symbols   | How to  \u003Cbr>Read It   |\n| Conditional   | Use the given  \u003Cbr>hypothesis and  \u003Cbr>conclusion.   | If m∠A=15,  \u003Cbr>then ∠A is  \u003Cbr>acute.   | p→q   | Ifp,then q.   |\n| Converse   | Exchange the  \u003Cbr>hypothesis and  \u003Cbr>the conclusion.   | If ∠A is  \u003Cbr>acute,then  \u003Cbr>m∠A=15.   | q→p   | If q,then p.   |\n| Inverse   | Negate both the  \u003Cbr>hypothesis and  \u003Cbr>the conclusion of  \u003Cbr>the conditional.   | If m∠A≠15,  \u003Cbr>then ∠A is not  \u003Cbr>acute.   |  | Ifnot p,  \u003Cbr>then not q.   |\n| Contrapositive   | Negate both the  \u003Cbr>hypothesis and  \u003Cbr>the conclusion  \u003Cbr>of the converse.   | If ∠A is not  \u003Cbr>acute,then  \u003Cbr>m∠A≠15.   |  | If not q,  ","cbCainBOBttErIBO","https://ap.wps.com/l/cbCainBOBttErIBO","pdf",1753231,20,"English","# Geometry Cheat Sheet\n## Chapter 1\n### Postulates and Angle Relationships\n### Constructions\n## Inductive Reasoning and Counterexample\n## Conditional Statements and Logic Laws\n## Theorem 2-1 Vertical Angles Theorem","[{\"question\":\"What is the Segment Addition Postulate and how is it used?\",\"answer\":\"If points A, B, and C are collinear and B is between A and C, then AB + BC = AC. It helps relate segment lengths along a line.\"},{\"question\":\"How do you construct congruent segments and congruent angles?\",\"answer\":\"For congruent segments, draw a ray with endpoint C, set the compass to AB, transfer the length to point C, and mark the intersection point. For congruent angles, draw an arc from vertex A to mark intersections, then transfer the corresponding arc length to the new ray and connect the needed points.\"},{\"question\":\"What are the converse, inverse, and contrapositive of a conditional statement?\",\"answer\":\"For a conditional p → q, the converse swaps hypothesis and conclusion (q → p), the inverse negates both (if not p then not q), and the contrapositive negates both with roles reversed (if not q then not p).\"},{\"question\":\"How do deductive reasoning tools like the Law of Detachment and Law of Syllogism work?\",\"answer\":\"The Law of Detachment states that if p → q is true and p is true, then q is true. The Law of Syllogism states that if p → q is true and q → r is true, then p → r is true.\"}]","Geometry Cheat Sheet - Chapter 1 - Key Concepts and Constructions | PDF",1791923788,7]