[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-571804-105":3,"detail-sidebar-cat-1-en-105":80,"doc-detail-571804-en":126},{"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":73,"head_meta":75,"extra_data":77,"updated_unix":79},105,"en","geo-reference-sheet-math-properties-formulas-geometry-trigonometry","Geo Reference Sheet - Math Properties, Formulas, Geometry & Trigonometry","","A geometry and algebra reference sheet compiling key theorems, property rules, and widely used formulas. It includes equality properties (addition, multiplication, reflexive, symmetric, transitive, subtraction, division, substitution), congruence properties, and parallel-line and distributive rules. Geometry sections cover segment/angle congruence, polygon angle theorems, triangle inequalities, triangle-sum and midsegment results, similarity/mean theorems, and coordinate-geometry equations like slope, distance, midpoint, and circle equations. Trigonometry and measurement formulas include right-triangle relations, sine/cosine/tangent identities, law of sines and cosines, circle arc/sector relations, perimeter/area/volume formulas, quadratic and conversion formulas, and temperature/units conversions.",{"@graph":14,"@context":72},[15,34,55],{"@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/paper-templates/","Paper 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listed on the reference sheet?","Question",{"text":62,"@type":63},"It lists addition, multiplication, reflexive, transitive, subtraction, division, symmetric, and substitution properties, each expressed as an if-then rule for equations.","Answer",{"name":65,"@type":60,"acceptedAnswer":66},"Which coordinate geometry formulas are included?",{"text":67,"@type":63},"The sheet includes slope, standard form of a line (Ax + By = C), slope-intercept form (y = mx + b), point-slope form, midpoint formula, standard circle equation, and distance formula.",{"name":69,"@type":60,"acceptedAnswer":70},"What trigonometry topics and formulas does the sheet cover?",{"text":71,"@type":63},"It covers sine/cosine/tangent ratios and their inverses, conversions between degrees and radians, complementary-angle identities, area formulas for triangles, the law of sines, and the law of cosines.","https://schema.org",{"og:url":32,"og:type":74,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":76,"canonical":32},"index,follow",{"doc_id":78,"site_id":7},571804,1792053086,{"code":4,"msg":81,"data":82},"success",[83,88,93,98,103,108,113,118,122],{"id":84,"doc_module":22,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},11,"Presentations",90,"presentations",{"id":89,"doc_module":22,"doc_module_name":25,"category_name":90,"show_sort_weight":91,"slug":92},12,"Resumes",80,"resumes",{"id":94,"doc_module":22,"doc_module_name":25,"category_name":95,"show_sort_weight":96,"slug":97},14,"Invoices",70,"invoices",{"id":99,"doc_module":22,"doc_module_name":25,"category_name":100,"show_sort_weight":101,"slug":102},15,"Posters",60,"posters",{"id":104,"doc_module":22,"doc_module_name":25,"category_name":105,"show_sort_weight":106,"slug":107},16,"Social 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 \nProperties  \nProperties of Equality  \nAddition Property of Equality  \nIf a = b, then a + c = b + c.  \nMultiplication Property of Equality  \nIf a = b, then a ⋅ c = b ⋅ c, c ≠ 0.  \nReflexive Property of Equality  \na = a  \nTransitive Property of Equality  \nIf a = b and b = c, then a = c.  \nSubtraction Property of Equality  \nIf a = b, then a − c = b − c.  \nDivision Property of Equality  \nIf a = b, then  = , c ≠ 0.  \nSymmetric Property of Equality  \nIf a = b, then b = a.  \nSubstitution Property of Equality  \nIf a = b, then a can be substituted for b (or b for a) in any equation or expression.  \nProperties of Segment and Angle Congruence  \nReflexive Property of Congruence  \nFor any segment AB, A—B ≅ A—B.  \nSymmetric  Property of  Congruence IfAB ≅ CD , then CD ≅ AB .  \nTransitive Property of Congruence  \nIfA—B ≅ C—Dand C—D ≅ E—F, then A—B ≅ E—F  \nFor any angleA, ∠ A ≅ ∠ A.  \nIf ∠ A ≅ ∠ B, then ∠ B ≅ ∠ A.  \nIf ∠ A ≅ ∠ B and ∠ B ≅ ∠ C, then ∠ A ≅ ∠ C.  \nOther Properties  \nTransitive Property of Parallel Lines  \nIf p 􀀆 q and q 􀀆 r, then p 􀀆 r.  \nDistributive Property  \nSum  \na(b + c) = ab + ac Difference  \na(b − c) = ab − ac  \nTriangle Inequalities  \nTriangle Inequality Theorem  \nBA   \nAB + BC > AC  \nAC + BC > AB AB + AC > BC  \nC  \nPythagorean Inequalities Theorem  \nC a B  \nA  \nC a B  \nIf c2 \u003C a2 + b2, then If c2 > a2 + b2, then △ABC is acute. △ABC is obtuse.  \nReference A91  \nFormulas  \nCoordinate Geometry  \nSlope  \nm = 22 −yx11  \nStandard form of a linear equation  \nAx + By = C  \nMidpoint Formula ( 1 +2x2 , 1 +2 y2 )  \nSlope-intercept form  \ny = mx + b  \nPoint-slope form  \ny − y 1 = m(x − x1)  \nStandard equation of a circle  \n(x − h)2 + ( y − k)2 = r2, with center (h, k) and radius r  \nDistance Formula  \nd = √(x2 − x1)2 + (y2 − y 1)2  \n——  \nPolygons  \nTriangle Sum Theorem  \nA  \nm∠ A + m∠ B + m∠ C = 180°  \nTriangle Midsegment Theorem  \nB  \nA  \nC  \n—  \nDE 􀀆 AC , DE = AC  \nPolygon Interior Angles Theorem  \nn = 6  \nm∠ 1 + m∠ 2 + . . . + m∠ n = (n − 2) ⋅ 180°  \nGeometric Mean (Altitude) Theorem  \nC  \nA D B  \nCD2 = AD ⋅ BD  \nExterior Angle Theorem  \nB  \n1  \nA C  \nm∠ 1 = m∠ A + m∠ B  \nTrapezoid Midsegment Theorem  \nD  \n—  \n—  \nC  \nMN 􀀆 AB , MN 􀀆 DC , MN = (AB + CD)  \nPolygon Exterior Angles Theorem  \n2 3  \n4  \n1  \n5  \nn = 5  \nm∠ 1 + m∠ 2 + . . . + m∠ n = 360°  \nGeometric Mean (Leg) Theorem  \nC  \nA D B  \nCB2 = DB ⋅AB AC2 = AD ⋅AB  \nA92 Reference  \nRight Triangles  \nPythagorean Theorem  \nb  \na2 + b2 = c2  \n45°-45°-90° Triangles  \nx  \nhypotenuse = leg ⋅√—2  \n30°-60°-90° Triangles  \nhyplongnulegse=shortrlegg 2—3  \nTrigonometry  \nRatios  \nB  \nA C  \nsin A  \nsin −1  \n=   \nBC  \n—  \nAB  \n=  \nm∠ A  \ncos A  \ncos −1  \n= AA  \nAA =  \nm∠ A  \ntanA  \ntan −1  \n= AA = m∠ A  \nConversion between degrees and radians  \n180° = π radians  \nSine and cosine of complementary angles  \nLet A and B be complementary angles. Then the following statements are true.  \nsinA = cos(90° − A) = cos B sin B = cos(90° − B) = cos Acos A = sin(90° − A) = sin B cos B = sin(90° − B) = cos A  \nAny Triangle  \nB  \nA b C  \nArea  \nArea = bc sinA  \nArea = ac sin B  \nArea = ab sin C  \nB  \nA b C  \nLaw of Sines  \n =  =   a  =  b  =  c  sin A sin B sin C  \nLaw of Cosines  \na2 = b2 + c2 − 2bc cos Ab2 = a2 + c2 − 2ac cos Bc2 = a2 + b2 − 2ab cos C  \nReference A93  \nCircles  \nArc length  \nArc length of  = ° ⋅2 πr  \nArea of a sector  \nArea of sector APB = ° ⋅ πr2  \nCentral angles  \nm∠ ACB = m  \nInscribed angles  \nm∠ ADB = m  \nTangent and intersected chord  \nm∠ 1 = m  \nm∠ 2 = m  \nAngles and Segments of Circles  \nTwo chords  \nC  \nA 1 E  \nBD  \nm∠ 1 = (m + m) EA ⋅ EB = EC ⋅ ED Tangent and secant  \nm∠ 1 = (m − m) EA2 = EC ⋅ ED  \nTwo secants  \nBA  \nE 1   \nC  \nD  \nm∠ 1 = (m − m) EA ⋅ EB = EC ⋅ ED Two tangents  \nm∠ 1 = (m − m) EA = EB  \nA94 Reference  \nPerimeter, Area, and Volume Formulas  \nRhombus/Kite  \nA = d1d2  \nPrism  \nL = Ph S = 2B + Ph V = Bh  \nCone  \nCylinder  \nL = 2 πrh  \nS = 2 πr2 + 2 πrh V = πr2h  \nL = πrℓ S = πr2 + πrℓ V = πr2h  \nRegular n-gon  \ns  \nA = aP or A = a ⋅ ns  \nPyramid  \nL ","cbCainltJ4HRfFv6","https://ap.wps.com/l/cbCainltJ4HRfFv6","pdf",214614,6,"English","# Properties of Equality\n## Properties of Segment and Angle Congruence\n## Other Properties\n# Triangle Inequalities and Pythagorean Inequalities\n# Coordinate Geometry Formulas\n## Polygons\n## Right Triangles\n# Trigonometry\n## Ratios and Identities\n## Law of Sines and Cosines\n# Circles\n## Arc length and Sector Area\n# Perimeter, Area, and Volume Formulas\n## Polygons and Solids\n# Other Formulas and Conversions\n## Quadratic Formula and Density\n## Units and Temperature Conversions","[{\"question\":\"What equality properties are listed on the reference sheet?\",\"answer\":\"It lists addition, multiplication, reflexive, transitive, subtraction, division, symmetric, and substitution properties, each expressed as an if-then rule for equations.\"},{\"question\":\"Which coordinate geometry formulas are included?\",\"answer\":\"The sheet includes slope, standard form of a line (Ax + By = C), slope-intercept form (y = mx + b), point-slope form, midpoint formula, standard circle equation, and distance formula.\"},{\"question\":\"What trigonometry topics and formulas does the sheet cover?\",\"answer\":\"It covers sine/cosine/tangent ratios and their inverses, conversions between degrees and radians, complementary-angle identities, area formulas for triangles, the law of sines, and the law of cosines.\"}]","Geo Reference Sheet - Math Properties, Formulas, Geometry & Trigonometry | PDF",1791923783]