Indiana Academic Standards 2020Geometry

Standards Correlation Guidance Document

Intentional alignment of instructional practices and curricular materials to the Indiana Academics Standards (IAS) is vital to improvingstudent outcomes. This guide is meant to encourage strong standards-based instruction when utilizing curricular materials not alignedto IAS but to Common Core State Standards (CCSS). Purchased curricula are not designed to perfectly align with IAS and often alignwith CCSS. Use of this guide will ensure strong alignment to IAS and foster critical conversations around instructional decisions.

Considerations for use:

● Identify the desired IAS;● Unpack the IAS, referencing the IDOE Math Framework;● Determine the correlating CCSS;● Consider the differences between IAS and learning objective from CCSS aligned curricular material;● Identify instructional gaps (in content or complexity) and consider strategies to supplement; and● Prioritize content in curricular material that is identified in the IAS.

IDOE’s Math Framework provides student success criteria, vertical planning, digital resources, and clarifying examples to considerwhen planning, implementing, and teaching IAS.

Updated May 20211

Indiana Academic Standards (IAS)2020

Common Core State Standards(CCSS)

Difference Between IAS 2020 andCCSS

Process Standards for MathematicsPS.1: Make sense of problems andpersevere in solving them.

Mathematically proficient students start byexplaining to themselves the meaning of aproblem and looking for entry points to itssolution. They analyze givens, constraints,relationships, and goals. They makeconjectures about the form and meaning ofthe solution and plan a solution pathway,rather than simply jumping into a solutionattempt. They consider analogous problemsand try special cases and simpler forms ofthe original problem in order to gain insightinto its solution. They monitor and evaluatetheir progress and change course ifnecessary. Mathematically proficientstudents check their answers to problemsusing a different method, and theycontinually ask themselves, “Does this makesense?” and "Is my answer reasonable?"They understand the approaches of othersto solving complex problems and identifycorrespondences between differentapproaches. Mathematically proficientstudents understand how mathematicalideas interconnect and build on one anotherto produce a coherent whole.

MP1: Make sense of problems andpersevere in solving them.

Mathematically proficient students start byexplaining to themselves the meaning of aproblem and looking for entry points to itssolution. They analyze givens, constraints,relationships, and goals. They makeconjectures about the form and meaning ofthe solution and plan a solution pathwayrather than simply jumping into a solutionattempt. They consider analogous problems,and try special cases and simpler forms ofthe original problem in order to gain insightinto its solution. They monitor and evaluatetheir progress and change course ifnecessary. Older students might, dependingon the context of the problem, transformalgebraic expressions or change the viewingwindow on their graphing calculator to getthe information they need. Mathematicallyproficient students can explaincorrespondences between equations, verbaldescriptions, tables, and graphs or drawdiagrams of important features andrelationships, graph data, and search forregularity or trends. Younger students mightrely on using concrete objects or pictures tohelp conceptualize and solve a problem.

IAS removes criteria involving a graphingcalculator and does not distinguish betweenyounger and older students.

Updated May 20212

Mathematically proficient students checktheir answers to problems using a differentmethod, and they continually askthemselves, "Does this make sense?" Theycan understand the approaches of others tosolving complex problems and identifycorrespondences between differentapproaches.

PS.2: Reason abstractly andquantitatively.

Mathematically proficient students makesense of quantities and their relationships inproblem situations. They bring twocomplementary abilities to bear on problemsinvolving quantitative relationships: theability to decontextualize—to abstract agiven situation and represent it symbolicallyand manipulate the representing symbols asif they have a life of their own, withoutnecessarily attending to their referents—andthe ability to contextualize, to pause asneeded during the manipulation process inorder to probe into the referents for thesymbols involved. Quantitative reasoningentails habits of creating a coherentrepresentation of the problem at hand;considering the units involved; attending tothe meaning of quantities, not just how tocompute them; and knowing and flexiblyusing different properties of operations andobjects.

MP.2: Reason abstractly andquantitatively.

Mathematically proficient students makesense of quantities and their relationships inproblem situations. They bring twocomplementary abilities to bear on problemsinvolving quantitative relationships: theability to decontextualize—to abstract agiven situation and represent it symbolicallyand manipulate the representing symbols asif they have a life of their own, withoutnecessarily attending to their referents—andthe ability to contextualize, to pause asneeded during the manipulation process inorder to probe into the referents for thesymbols involved. Quantitative reasoningentails habits of creating a coherentrepresentation of the problem at hand;considering the units involved; attending tothe meaning of quantities, not just how tocompute them; and knowing and flexiblyusing different properties of operations andobjects.

No content differences identified.

Updated May 20213

PS.3: Construct viable arguments andcritique the reasoning of others.

Mathematically proficient studentsunderstand and use stated assumptions,definitions, and previously establishedresults in constructing arguments. Theymake conjectures and build a logicalprogression of statements to explore thetruth of their conjectures. They analyzesituations by breaking them into cases andrecognize and use counterexamples. Theyorganize their mathematical thinking, justifytheir conclusions and communicate them toothers, and respond to the arguments ofothers. They reason inductively about data,making plausible arguments that take intoaccount the context from which the dataarose. Mathematically proficient students arealso able to compare the effectiveness oftwo plausible arguments, distinguish correctlogic or reasoning from that which is flawed,and—if there is a flaw in anargument—explain what it is. They justifywhether a given statement is true always,sometimes, or never. Mathematicallyproficient students participate andcollaborate in a mathematics community.They listen to or read the arguments ofothers, decide whether they make sense,and ask useful questions to clarify orimprove the arguments.

MP.3: Construct viable arguments andcritique the reasoning of others.

Mathematically proficient studentsunderstand and use stated assumptions,definitions, and previously establishedresults in constructing arguments. Theymake conjectures and build a logicalprogression of statements to explore thetruth of their conjectures. They are able toanalyze situations by breaking them intocases, and can recognize and usecounterexamples. They justify theirconclusions, communicate them to others,and respond to the arguments of others.They reason inductively about data, makingplausible arguments that take into accountthe context from which the data arose.Mathematically proficient students are alsoable to compare the effectiveness of twoplausible arguments, distinguish correct logicor reasoning from that which is flawed,and—if there is a flaw in anargument—explain what it is. Elementarystudents can construct arguments usingconcrete referents such as objects,drawings, diagrams, and actions. Sucharguments can make sense and be correct,even though they are not generalized ormade formal until later grades. Later,students learn to determine domains towhich an argument applies. Students at allgrades can listen or read the arguments ofothers, decide whether they make sense,

IAS includes the justification of statementsthat are true always, sometimes, or never.IAS includes collaboration in a mathematicscommunity and does not distinguishbetween younger and older students.

Updated May 20214

and ask useful questions to clarify orimprove the arguments.

PS.4: Model with mathematics.

Mathematically proficient students apply themathematics they know to solve problemsarising in everyday life, society, and theworkplace using a variety of appropriatestrategies. They create and use a variety ofrepresentations to solve problems and toorganize and communicate mathematicalideas. Mathematically proficient studentsapply what they know and are comfortablemaking assumptions and approximations tosimplify a complicated situation, realizingthat these may need revision later. They areable to identify important quantities in apractical situation and map theirrelationships using such tools as diagrams,two-way tables, graphs, flowcharts andformulas. They analyze those relationshipsmathematically to draw conclusions. Theyroutinely interpret their mathematical resultsin the context of the situation and reflect onwhether the results make sense, possiblyimproving the model if it has not served itspurpose.

MP.4: Model with mathematics.

Mathematically proficient students can applythe mathematics they know to solveproblems arising in everyday life, society,and the workplace. In early grades, thismight be as simple as writing an additionequation to describe a situation. In middlegrades, a student might apply proportionalreasoning to plan a school event or analyzea problem in the community. By high school,a student might use geometry to solve adesign problem or use a function to describehow one quantity of interest depends onanother. Mathematically proficient studentswho can apply what they know arecomfortable making assumptions andapproximations to simplify a complicatedsituation, realizing that these may needrevision later. They are able to identifyimportant quantities in a practical situationand map their relationships using such toolsas diagrams, two-way tables, graphs,flowcharts and formulas. They can analyzethose relationships mathematically to drawconclusions. They routinely interpret theirmathematical results in the context of thesituation and reflect on whether the resultsmake sense, possibly improving the model ifit has not served its purpose.

IAS does not distinguish between youngerand older students.

Updated May 20215

PS.5: Use appropriate tools strategically.

Mathematically proficient students considerthe available tools when solving amathematical problem. These tools mightinclude pencil and paper, models, a ruler, aprotractor, a calculator, a spreadsheet, acomputer algebra system, a statisticalpackage, or dynamic geometry software.Mathematically proficient students aresufficiently familiar with tools appropriate fortheir grade or course to make sounddecisions about when each of these toolsmight be helpful, recognizing both the insightto be gained and their limitations.Mathematically proficient students identifyrelevant external mathematical resources,such as digital content, and use them topose or solve problems. They usetechnological tools to explore and deepentheir understanding of concepts and tosupport the development of learningmathematics. They use technology tocontribute to concept development,simulation, representation, reasoning,communication and problem solving.

MP.5: Use appropriate tools strategically.

Mathematically proficient students considerthe available tools when solving amathematical problem. These tools mightinclude pencil and paper, concrete models, aruler, a protractor, a calculator, aspreadsheet, a computer algebra system, astatistical package, or dynamic geometrysoftware. Proficient students are sufficientlyfamiliar with tools appropriate for their gradeor course to make sound decisions aboutwhen each of these tools might be helpful,recognizing both the insight to be gained andtheir limitations. For example,mathematically proficient high schoolstudents analyze graphs of functions andsolutions generated using a graphingcalculator. They detect possible errors bystrategically using estimation and othermathematical knowledge. When makingmathematical models, they know thattechnology can enable them to visualize theresults of varying assumptions, exploreconsequences, and compare predictionswith data. Mathematically proficient studentsat various grade levels are able to identifyrelevant external mathematical resources,such as digital content located on a website,and use them to pose or solve problems.They are able to use technological tools toexplore and deepen their understanding ofconcepts.

IAS does not distinguish between youngerand older students.

Updated May 20216

PS.6: Attend to precision.

Mathematically proficient studentscommunicate precisely to others. They useclear definitions, including precision. correctmathematical language, in discussion withothers and in their own reasoning. Theystate the meaning of the symbols theychoose, including using the equal signconsistently and appropriately. They expresssolutions clearly and logically by using theappropriate mathematical terms andnotation. They specify units of measure andlabel axes to clarify the correspondence withquantities in a problem. They calculateaccurately and efficiently and check thevalidity of their results in the context of theproblem. They express numerical answerswith a degree of precision appropriate for theproblem context.

MP.6: Attend to precision.

Mathematically proficient students try tocommunicate precisely to others. They try touse clear definitions in discussion withothers and in their own reasoning. Theystate the meaning of the symbols theychoose, including using the equal signconsistently and appropriately. They arecareful about specifying units of measure,and labeling axes to clarify thecorrespondence with quantities in a problem.They calculate accurately and efficiently,express numerical answers with a degree ofprecision appropriate for the problemcontext. In the elementary grades, studentsgive carefully formulated explanations toeach other. By the time they reach highschool they have learned to examine claimsand make explicit use of definitions.

IAS does not distinguish between youngerand older students.

PS.7: Look for and make use of structure.

Mathematically proficient students lookclosely to discern a pattern or structure.They step back for an overview and shiftperspective. They recognize and useproperties of operations and equality. Theyorganize and classify geometric shapesbased on their attributes. They seeexpressions, equations, and geometricfigures as single objects or as beingcomposed of several objects.

MP.7: Look for and make use of structure.

Mathematically proficient students lookclosely to discern a pattern or structure.Young students, for example, might noticethat three and seven more is the sameamount as seven and three more, or theymay sort a collection of shapes according tohow many sides the shapes have. Later,students will see 7 × 8 equals the wellremembered 7 × 5 + 7 × 3, in preparation forlearning about the distributive property. Inthe expression x2 + 9x + 14, older studentscan see the 14 as 2 × 7 and the 9 as 2 + 7.

IAS has removed examples and does notdistinguish between younger and olderstudents.

Updated May 20217

They recognize the significance of anexisting line in a geometric figure and canuse the strategy of drawing an auxiliary linefor solving problems. They also can stepback for an overview and shift perspective.They can see complicated things, such assome algebraic expressions, as singleobjects or as being composed of severalobjects. For example, they can see 5 - 3(x -y)2 as 5 minus a positive number times asquare and use that to realize that its valuecannot be more than 5 for any real numbersx and y.

PS.8: Look for and express regularity inrepeated reasoning.

Mathematically proficient students notice ifcalculations are repeated and look forgeneral methods and shortcuts. They noticeregularity in mathematical problems andtheir work to create a rule orformula.Mathematically proficient studentsmaintain oversight of the process, whileattending to the details as they solve aproblem. They continually evaluate thereasonableness of their intermediate results.

MP.8: Look for and express regularity inrepeated reasoning.

Mathematically proficient students notice ifcalculations are repeated, and look both forgeneral methods and for shortcuts. Upperelementary students might notice whendividing 25 by 11 that they are repeating thesame calculations over and over again, andconclude they have a repeating decimal. Bypaying attention to the calculation of slopeas they repeatedly check whether points areon the line through (1, 2) with slope 3,middle school students might abstract theequation (y - 2)/(x - 1) = 3. Noticing theregularity in the way terms cancel whenexpanding (x - 1)(x + 1), (x - 1)(x2 + x + 1),and (x - 1)(x3 + x2 + x + 1) might lead them tothe general formula for the sum of ageometric series. As they work to solve aproblem, mathematically proficient students

IAS has removed examples and does notdistinguish between younger and olderstudents.

Updated May 20218

maintain oversight of the process, whileattending to the details. They continuallyevaluate the reasonableness of theirintermediate results.

Updated May 20219

Indiana Academic Standards (IAS)2020

Common Core State Standards(CCSS)

Difference Between IAS 2020 andCCSS

Logic and ProofsG.LP.1: Understand and describe thestructure of and relationships within anaxiomatic system (undefined terms,definitions, axioms and postulates, methodsof reasoning, and theorems). Understandthe differences among supporting evidence,counterexamples, and actual proofs.

No CCSS equivalent.

G.LP.2: Use precise definitions for angle,circle, perpendicular lines, parallel lines, andline segment, based on the undefinednotions of point, line, and plane. Usestandard geometric notation.

HSG.CO.A.1: Know precise definitions ofangle, circle, perpendicular line, parallel line,and line segment, based on the undefinednotions of point, line, distance along a line,and distance around a circular arc.

IAS omits distance along a line and distancearound a circular arc as undefined notions;requires the use of precise definitions notsimply the knowledge of them.

G.LP.3: State, use, and examine the validityof the converse, inverse, and contrapositiveof conditional (“if – then”) and bi-conditional(“if and only if”) statements.

No CCSS equivalent.

G.LP.4: Understand that proof is the meansused to demonstrate whether a statement istrue or false mathematically. Developgeometric proofs, including those involvingcoordinate geometry, using two-column,paragraph, and flow chart formats.

HSG.GPE.B.4: Use coordinates to provesimple geometric theorems algebraically.

IAS extends to two-column proofs,paragraph proofs, and flow chart formats ofproof; requires students to develop anunderstanding of the purpose of proof inmathematics.

Updated May 202110

Indiana Academic Standards (IAS)2020

Common Core State Standards(CCSS)

Difference Between IAS 2020 andCCSS

Points, Lines, and AnglesG.PL.1: Prove and apply theorems aboutlines and angles, including the following:

● Vertical angles are congruent.

● When a transversal crosses parallellines, alternate interior angles arecongruent, alternate exterior anglesare congruent, and correspondingangles are congruent.

● When a transversal crosses parallellines, same side interior angles aresupplementary.

● Points on a perpendicular bisector ofa line segment are exactly thoseequidistant from the endpoints of thesegment.

HSG.CO.B.9: Prove theorems about linesand angles. Theorems include: verticalangles are congruent; when a transversalcrosses parallel lines, alternate interiorangles are congruent and correspondingangles are congruent; points on aperpendicular bisector of a line segment areexactly those equidistant from thesegment’s endpoints.

IAS adds that when a transversal crossesparallel lines, alternate exterior angles arecongruent and same side interior angles aresupplementary.

G.PL.2: Explore the relationships of theslopes of parallel and perpendicular lines.Determine if a pair of lines are parallel,perpendicular, or neither by comparing theslopes in coordinate graphs and equations.

HSG.GPE.B.5: Prove the slope criteria forparallel and perpendicular lines and usethem to solve geometric problems.

IAS emphasizes exploration of slopes ofparallel and perpendicular lines rather thanformal proof.

G.PL.3: Use tools to explain and justify theprocess to construct congruent segmentsand angles, angle bisectors, perpendicular

HSG.CO.D.12: Make formal geometricconstructions with a variety of tools andmethods (compass and straightedge, string,reflective devices, paper folding, dynamic

IAS emphasizes explaining and justifyingthe process to construct, rather than fluencyin construction.

Updated May 202111

bisectors, altitudes, medians, and paralleland perpendicular lines.

geometric software, etc.). Copying asegment; copying an angle; bisecting asegment; bisecting an angle; constructingperpendicular lines, including theperpendicular bisector of a line segment;and constructing a line parallel to a givenline through a point not on the line.

G.PL.4: Develop the distance formula usingthe Pythagorean Theorem. Find the lengthsand midpoints of line segments in thetwo-dimensional coordinate system.

HSG.GPE.B.7: Use coordinates to computeperimeters of polygons and areas oftriangles and rectangles, e.g., using thedistance formula.

IAS requires students to develop thedistance formula using the PythagoreanTheorem; extends to include findingmidpoints of segments.

Updated May 202112

Indiana Academic Standards (IAS)2020

Common Core State Standards(CCSS)

Difference Between IAS 2020 andCCSS

TrianglesG.T.1: Prove and apply theorems abouttriangles, including the following:

● Measures of interior angles of atriangle sum to 180°.

● The Isosceles Triangle Theorem andits converse.

● The Pythagorean Theorem.

● The segment joining midpoints of twosides of a triangle is parallel to thethird side and half the length.

● A line parallel to one side of a triangledivides the other two proportionally,and its converse.

● The Angle Bisector Theorem.

HSG.CO.C.10: Prove theorems abouttriangles. Theorems include: measures ofinterior angles of a triangle sum to 180°;base angles of isosceles triangles arecongruent; the segment joining midpoints oftwo sides of a triangle is parallel to the thirdside and half the length; the medians of atriangle meet at a point.

HSG.SRT.B.4: Prove theorems abouttriangles. Theorems include: a line parallelto one side of a triangle divides the othertwo proportionally, and conversely; thePythagorean Theorem proved using trianglesimilarity.

IAS specifies the Angle Bisector Theorem;omits the medians of a triangle meet at apoint; omits using similarity to prove thePythagorean Theorem.

G.T.2: Explore and explain how the criteriafor triangle congruence (ASA, SAS, AAS,SSS, and HL) follow from the definition ofcongruence in terms of rigid motions.

HSG.CO.B.8: Explain how the criteria fortriangle congruence (ASA, SAS, and SSS)follow from the definition of congruence interms of rigid motions.

IAS includes AAS and HL criteria.

G.T.3: Use tools to explain and justify theprocess to construct congruent triangles.

HSG.CO.B.7: Use the definition ofcongruence in terms of rigid motions toshow that two triangles are congruent if and

IAS allows for tools in lieu of definitions;emphasizes explaining and justifying the

Updated May 202113

only if corresponding pairs of sides andcorresponding pairs of angles arecongruent.

HSG.CO.D.12: Make formal geometricconstructions with a variety of tools andmethods (compass and straightedge, string,reflective devices, paper folding, dynamicgeometric software, etc.). Copying asegment; copying an angle; bisecting asegment; bisecting an angle; constructingperpendicular lines, including theperpendicular bisector of a line segment;and constructing a line parallel to a givenline through a point not on the line.

process to construct, rather than fluency inconstruction; specific to triangles.

G.T.4: Use the definition of similarity interms of similarity transformations, todetermine if two given triangles are similar.Explore and develop the meaning ofsimilarity for triangles.

HSG.SRT.A.2: Given two figures, use thedefinition of similarity in terms of similaritytransformations to decide if they are similar;explain using similarity transformations themeaning of similarity for triangles as theequality of all corresponding pairs of anglesand the proportionality of all correspondingpairs of sides.

HSG.SRT.A.3: Use the properties ofsimilarity transformations to establish the AAcriterion for two triangles to be similar.

IAS is specific to triangles; emphasisesexploration over simply explaining; does notexplicitly cite the AA criterion.

G.T.5: Use congruent and similar trianglesto solve real-world and mathematicalproblems involving sides, perimeters, andareas of triangles.

HSG.SRT.B.5: Use congruence andsimilarity criteria for triangles to solveproblems and to prove relationships ingeometric figures.

IAS omits proving relationships in geometricfigures.

Updated May 202114

G.T.6: Prove and apply the inequalitytheorems, including the following:

● Triangle inequality.

● Inequality in one triangle.

● The hinge theorem and its converse.

No CCSS equivalent.

G.T.7: Explore the relationships that existwhen the altitude is drawn to thehypotenuse of a right triangle. Understandand use the geometric mean to solve formissing parts of triangles.

No CCSS equivalent.

G.T.8: Understand that by similarity, sideratios in right triangles are properties of theangles in the triangle, leading to definitionsof trigonometric ratios for acute angles.

HSG.SRT.C.6: Understand that by similarity,side ratios in right triangles are properties ofthe angles in the triangle, leading todefinitions of trigonometric ratios for acuteangles.

No content differences identified.

G.T.9: Use trigonometric ratios (sine, cosineand tangent) and the Pythagorean Theoremto solve real-world and mathematicalproblems involving right triangles.

HSG.SRT.C.8: Use trigonometric ratios andthe Pythagorean Theorem to solve righttriangles in applied problems.

IAS is limited to sine, cosine, and tangent.

G.T.10: Explore the relationship betweenthe sides of special right triangles (30° - 60°and 45° - 45°) and use them to solvereal-world and other mathematicalproblems.

No CCSS equivalent.

Updated May 202115

Indiana Academic Standards (IAS)2020

Common Core State Standards(CCSS)

Difference Between IAS 2020 andCCSS

Quadrilaterals and Other PolygonsG.QP.1: Prove and apply theorems aboutparallelograms, including those involvingangles, diagonals, and sides.

HSG.CO.C.11: Prove theorems aboutparallelograms. Theorems include: oppositesides are congruent, opposite angles arecongruent, the diagonals of a parallelogrambisect each other, and conversely,rectangles are parallelograms withcongruent diagonals.

No content differences identified.

G.QP.2: Prove that given quadrilaterals areparallelograms, rhombuses, rectangles,squares, kites, or trapezoids. Includecoordinate proofs of quadrilaterals in thecoordinate plane.

No CCSS equivalent.

G.QP.3: Develop and use formulas to findmeasures of interior and exterior angles ofpolygons.

No CCSS equivalent.

G.QP.4: Identify types of symmetry ofpolygons, including line, point, rotational,and self-congruencies.

No CCSS equivalent.

G.QP.5: Compute perimeters and areas ofpolygons in the coordinate plane to solvereal-world and other mathematicalproblems.

HSG.GPE.B.7: Use coordinates to computeperimeters of polygons and areas oftriangles and rectangles, e.g., using thedistance formula.

No content differences identified.

Updated May 202116

G.QP.6: Develop and use formulas for areasof regular polygons.

No CCSS equivalent.

Updated May 202117

Indiana Academic Standards (IAS)2020

Common Core State Standards(CCSS)

Difference Between IAS 2020 andCCSS

CirclesG.CI.1: Define, identify and userelationships among the following: radius,diameter, arc, measure of an arc, chord,secant, tangent, congruent circles, andconcentric circles.

No CCSS equivalent.

G.CI.2: Derive the fact that the length of thearc intercepted by an angle is proportionalto the radius; derive the formula for the areaof a sector.

HSG.C.B.5: Derive using similarity the factthat the length of the arc intercepted by anangle is proportional to the radius, anddefine the radian measure of the angle asthe constant of proportionality; derive theformula for the area of a sector.

IAS omits using similarity; omit defining theradian measure of the angle as the constantof proportionality.

G.CI.3: Explore and use relationshipsamong inscribed angles, radii, and chords,including the following:

● The relationship that exists betweencentral, inscribed, and circumscribedangles.

● Inscribed angles on a diameter areright angles.

● The radius of a circle is perpendicularto a tangent where the radiusintersects the circle.

HSG.C.A.2: Identify and describerelationships among inscribed angles, radii,and chords. Include the relationshipbetween central, inscribed, andcircumscribed angles; inscribed angles on adiameter are right angles; the radius of acircle is perpendicular to the tangent wherethe radius intersects the circle.

No content difference identified.

Updated May 202118

G.CI.4: Solve real-world and othermathematical problems that involve findingmeasures of circumference, areas of circlesand sectors, and arc lengths and relatedangles (central, inscribed, and intersectionsof secants and tangents).

No CCSS equivalent.

G.CI.5: Use tools to explain and justify theprocess to construct a circle that passesthrough three given points not on a line, atangent line to a circle through a point onthe circle, and a tangent line from a pointoutside a given circle to the circle.

HSG.C.A.4: Construct a tangent line from apoint outside a given circle to the circle.

IAS additionally requires students toconstruct a circle that passes through threegiven points not on a line and a tangent lineto a circle through a point on the circle.

G.CI.6: Use tools to construct the inscribedand circumscribed circles of a triangle.Prove properties of angles for aquadrilateral inscribed in a circle.

HSG.C.A.3: Construct the inscribed andcircumscribed circles of a triangle, andprove properties of angles for a quadrilateralinscribed in a circle.

No content difference identified.

Updated May 202119

Indiana Academic Standards (IAS)2020

Common Core State Standards(CCSS)

Difference Between IAS 2020 andCCSS

TransformationsG.TR.1: Use geometric descriptions of rigidmotions to transform figures and to predictand describe the results of translations,reflections and rotations on a given figure.Describe a motion or series of motions thatwill show two shapes are congruent.

HSG.CO.A.5: Given a geometric figure anda rotation, reflection, or translation, draw thetransformed figure using, e.g., graph paper,tracing paper, or geometry software. Specifya sequence of transformations that will carrya given figure onto another.

HSG.CO.A.6: Use geometric descriptions ofrigid motions to transform figures and topredict the effect of a given rigid motion on agiven figure; given two figures, use thedefinition of congruence in terms of rigidmotions to decide if they are congruent.

G.TR.1 extends beyond prediction andrequires students to describe results.

G.TR.2: Verify experimentally the propertiesof dilations given by a center and a scalefactor. Understand the dilation of a linesegment is longer or shorter in the ratiogiven by the scale factor.

HSG.SRT.A.1: Verify experimentally theproperties of dilations given by a center anda scale factor.

HSG.SRT.A.1.B: The dilation of a linesegment is longer or shorter in the ratiogiven by the scale factor.

No content differences identified.

Updated May 202120

Indiana Academic Standards (IAS)2020

Common Core State Standards(CCSS)

Difference Between IAS 2020 andCCSS

Three-Dimensional SolidsG.TS.1: Create a net for a giventhree-dimensional solid. Describe thethree-dimensional solid that can be madefrom a given net (or pattern).

No CCSS equivalent.

G.TS.2: Explore and use symmetries ofthree-dimensional solids to solve problems.

No CCSS equivalent.

G.TS.3: Explore properties of congruent andsimilar solids, including prisms, regularpyramids, cylinders, cones, and spheresand use them to solve problems.

No CCSS equivalent.

G.TS.4: Solve real-world and othermathematical problems involving volumeand surface area of prisms, cylinders,cones, spheres, and pyramids, includingproblems that involve composite solids andalgebraic expressions.

HSG.GMD.A.3: Use volume formulas forcylinders, pyramids, cones, and spheres tosolve problems.

G.TS.4 includes surface area; includesprisms; emphasizes composite solids andincluding algebraic expressions.

G.TS.5: Apply geometric methods to createand solve design problems.

HSG.MG.A.3: Apply geometric methods tosolve design problems.

G.TS.5 extends to create.

Updated May 202121