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LSU College Readiness ProgramCOURSE PROFILE with LMSCOURSE NAME:High School GeometryPRIMARY ONLINE CONTENT SOURCE:Geometry in MyMathLabElayn Martin-GayCOURSE/UNIT CREDIT:1 Carnegie UnitGRADE(S):8, 9, or 10PREREQUISITE(S):Successful Completion of Algebra ICHAPTERS1 - The Beginning of Geometry7 - Similarity2 - Introduction to Reasoning and Proofs8 - Transformations3 - Parallel and Perpendicular Lines9 - Right Triangles and Trigonometry4 - Triangles and Congruence10 - Area5 - Special Properties of Triangles11 - Surface Area and Volume6 - Quadrilaterals12 - Circles and Other Conic SectionsSECTION NAMES (NUMBER OF EXERCISES), LEARNING OBJECTIVES, AND LOUISIANA MATHEMATICS STANDARDS CORRELATIONS CHAPTER 1: The Beginning of Geometry 1.2 Geometry – A Mathematical System (18)Understand how a mathematical system, like geometry, is formed.1.3 Points, Lines, and Planes (51)Learn the basic terms and postulates of geometryGeom.G.11.4 Segments and Their Measures (27)Determine where a point is on a lineUnderstand the measure of segmentsDetermine whether segments are congruentUse segment postulates and algebra to find segment lengthsGeom.G.11.5 Angles and Their Measures (25)Understand the measure of anglesUse algebra and the Angle Addition Postulate to solve applicationsGeom.G.11.6 Angle Pairs and Their Relationships (46)Learn special relationships between pairs of anglesUse algebra to find angle measures 1.7 Midpoint and Distance Formulas (35)Find the midpoint of a segmentFind the endpoint of a segmentFind the distance between two points on the coordinate planeFind the midpoint and distance of two pointsGeom.G.298.G.81.8 Basic Geometry Constructions (25)Make basic constructions using a straight edge and a compassGeom.G.12CHAPTER 2: Introduction to Reasoning and Proofs2.1 Perimeter, Circumference, and Area (34)Find the perimeter of circumference of basic shapesFind the area of basic shapesDetermine whether a situation is discussing area or perimeterDetermine the perimeter and areaUnderstand the concepts of perimeter and area Geom.G.302.2 Patterns and Inductive Reasoning (39)Use logic to understand patternsUnderstand and use inductive reasoningForm conjectures and find counterexamples2.3 Conditional Statements (31)Recognize conditional statements and their partsWrite the negation of a statementWrite converses, inverses, and contrapositives of conditional statements2.4 Biconditional Statements and Definitions (26)Write and understand biconditional statementsIdentify and understand good definitionsWrite conditional statements2.5 Deductive Reasoning (28)Review conditional, converse, inverse, and contrapositive statementsUnderstand and use the Law of DetachmentUnderstand and use the Law of SyllogismUnderstand and use the Law of Detachment and the Law of SyllogismUnderstand different types of reasoning2.6 Properties of Equality and Two-Column Proofs (33)Use properties of equality to justify reasons for stepsWrite a two-column proofGeom.G.92.7 Proving Theorems About Angles (29)Prove and uses theorems about anglesGeom.G.9CHAPTER 3: Parallel and Perpendicular Lines3.1 Lines and Angles (32)Identify relationships between lines and planesLearn the names of angles formed by lines and a transversalGeom.G.18.G.5 3.2 Proving Lines are Parallel (43)Use theorems to prove that two lines are parallelUse algebra to find the measures of angles needed so that lines are parallel.Understand the concepts of proofsGeom.G.98.G.53.3 Parallel Lines and Angles Formed by Transversals (38)Prove and use theorems about parallel lines cut by a transversalUse algebra to find measures of angles formed by parallel linesGeom.G.93.4 Proving Theorems: Parallel and Perpendicular Lines (22)Use and prove theorems about parallel and perpendicular linesUse algebra to find measures of angles related to perpendicular linesGeom.G.9Geom.G.343.5 Constructing Parallel an Perpendicular Lines (12)Construct parallel and perpendicular linesConstruct geometric shapes Geom.G.127.G.2 3.6 Coordinate Geometry – The Slope of a Line (32)Find the slope of a lineInterpret the slope-intercept form in an applicationCompare the slopes of parallel and perpendicular linesGeom.G.28Geom.G.34AlgI.SP.58.EE.63.7 Coordinate Geometry – Equations of Lines (26)Use the slope-intercept formUse the point-slope formWrite the equations of vertical and horizontal linesFind the equations of parallel and perpendicular linesUnderstand the concepts of parallel and perpendicular linesFind the equation of the perpendicular bisector of a line segmentGeom.G.28CHAPTER 4: Triangles and Congruence4.1 Types of Triangles (49)Learn the vocabulary of trianglesClassify triangles by angles and sidesFind angle measures of trianglesGeom.G.108.G.54.2 Congruent Figures (28)Identify corresponding parts in congruent figuresProve triangles are congruentGeom.G.184.3 Congruent Triangles by SSS and SAS (30)Determine parts of a triangle using a drawingProve two triangles are congruent using the SSS and SAS postulatesUse the distance formula to determine if two triangles are congruentUnderstand the meaning of the SSS and SAS postulatesGeom.G.184.4 Congruent Triangles by ASA and AAS (43)Prove two triangles are congruent using ASA postulates and the AAS theoremIdentify when to use SSS, SAS, ASA, or AAS to prove triangles congruentUse postulates and theorems of congruence to find missing values in a triangleGeom.G.184.5 Proofs Using Congruent Triangles (41)Identify common parts of overlapping trianglesUse triangle congruence and corresponding parts of congruent trianglesProve two triangles are congruent using other congruent trianglesDetermine the measure of missing angles and sides of congruent trianglesGeom.G.18Geom.G.344.6 Isosceles, Equilateral, and Right Triangles (51)Determine if triangles are congruentUse properties of isosceles and equilateral trianglesUse properties of right trianglesUse multiple properties of triangles to solveConstruct trianglesGeom.G.10Geom.G.18Geom.G.34CHAPTER 5: Special Properties of Triangles5.1 Perpendicular and Angle Bisectors (26)Use perpendicular bisectors to solve problemsUse angle bisectors to solve problemsGeom.G.9Geom.G.12Geom.G.185.2 Bisectors of a Triangle (32)Identify the differences between the circumcenter and the incenter of a triangleUse properties of perpendicular bisectors of sides of a triangleUse properties of angle bisectors of the angles of a triangleUse properties of both perpendicular bisectors and angle bisectorsGeom.G.24Geom.G.345.3 Medians and Altitudes of a Triangle (33)Identify differences between medians and altitudes of trianglesUse properties of the medians of a triangleUse properties of the altitudes of a triangleGeom.G.10Geom.G.275.4 Midsegments of Triangles (24)Use properties of midsegments of trianglesUse coordinate geometry with midsegmentsSolve applications of midsegmentsGeom.G.10Geom.G.12Geom.G.27Geom.G.345.5 Indirect Proofs and Inequalities in One Triangle (41)Use indirect reasoning to write proofsLearn the triangle relationship between length of a side and size of its opposite angleUse the triangle inequality theoremGeom.G.105.6 Inequalities in Two Triangles (21)Use the Hinge Theorem and its converse to compare measures of sides and anglesGeom.G.10Geom.G.34CHAPTER 6: Quadrilaterals6.1 Polygons (26)Define and name polygonsFind the sum of the measures of the interior angles of a quadrilateral 6.2 Parallelograms (42)Use relationships among sides and angles of parallelogramsUse relationships among consecutive angles and diagonals of parallelogramsGeom.G.11Geom.G.346.3 Proving that a Quadrilateral is a Parallelogram (17)Determine whether quadrilaterals are parallelogramsUse coordinate geometry with parallelogramsGeom.G.11Geom.G.27Geom.G.346.4 Rhombuses, Rectangles, and Squares (31)Define and classify special types of parallelogramsUse properties of diagonals of rhombuses, rectangles, and squaresUse properties of diagonals to form rhombuses, rectangles, and squaresGeom.G.11 6.5 Trapezoids and Kites (26)Use properties of trapezoidsUse properties of kitesGeom.G.18CHAPTER 7: Similarity7.1 Rates and Proportions (38)Write ratios as fractionsWrite ratios in simplest formUnderstand and work with extended ratiosSolve proportionsUnderstand and work with proportions7.RP.2 7.2 Proportion Properties and Problem Solving (41)Use properties of proportions to write equivalent proportionsSolve problems by writing proportions7.RP.2 7.3 Similar Polygons (38)Identify similar polygonsUse similar polygons to solve applicationsUnderstand the concepts of similar polygonsMake scaled drawingsGeom.G.187.4 Proving Triangles are Similar (35)Use the AA~ Postulate and the SAS~ and SSS~ TheoremUse similarity to find indirect measurementsFind the measurements of similar figuresGeom.G.17Geom.G.187.5 Geometric Mean and Similarity in Right Triangles (28)Use altitudes of right triangles to prove similarityFind the geometric mean of the lengths of segments in a right triangleSolve applications involving right trianglesUnderstand the concepts of right trianglesGeom.G.17Geom.G.187.6 Additional Proportions in Triangles (32)Use the Side-Splitter TheoremUse the Triangle-Angle-Bisector TheoremUnderstand the properties of parallelogramsGeom.G.17Geom.G.18CHAPTER 8: Transformations8.1 Rigid Transformations (9)Identify rigid transformations of isometriesName images and corresponding partsUse isometries to determine values of variablesGeom.G.158.2 Translations (16)Find translation images of figuresWrite ordered-pair translation rulesSolve application problems involving translationsSolve conceptual problems involving translationsGeom.G.2Geom.G.68.3 Reflections (21)Find reflection images of figuresIdentify and use line symmetrySolve application problems involving reflectionsSolve conceptual problems involving reflectionsGeom.G.2Geom.G.5Geom.G.68.4 Rotations (21)Draw and identify rotation images of figuresFind angles of rotationIdentify symmetriesGeom.G.2Geom.G.68.5 Dilations (16)Understand dilation images of figuresGeom.G.2Geom.G.148.6 Compositions of Reflections (17)Find compositions of reflections, including glide reflectionsClassify isometriesWork with kaleidoscope imagesProve properties of transformationsGeom.G.2Geom.G.4Geom.G.5Geom.G.6CHAPTER 9: Right Triangles and Trigonometry9.1 Pythagorean Theorem and its Converse (27)Use the Pythagorean TheoremUse the converse of the Pythagorean TheoremSolve application problemsGeom.G.10Geom.G.219.2 Special Right Triangles (18)Use the properties of 45-45-90 trianglesUse the properties of 30-60-90 trianglesUse the properties of special triangles to find the missing parts of geometric figuresSolve application problemsGeom.G.10Geom.G.19Geom.G.21Geom.G.349.3 Trigonometric Ratios (33)Write the ratios for sine, cosine, and tangent given a right triangleApproximate values for the sine, cosine, and tangent of an angleUse sine, cosine, and tangent ratios to determine side lengths in right trianglesApproximate angle measures given the sine, cosine, or tangent valueUse the sine, cosine, and tangent ratios to determine angle measure in right trianglesWrite the ratios for secant, cosecant, and cotangent given a right triangleSolve application problemsGeom.G.19Geom.G.20Geom.G.21Geom.G.349.4 Solving Right Triangles (21)Solve right trianglesUse angle of elevation and depression to solve problemsSolve application problemsGeom.G.219.5 Vectors (24)Describe vectorsSketch vectorsFind the magnitude and direction of a vectorAdd vectorsWrite the resultant of two vectors as an ordered pair and sketchUse vectors to solve application problems9.6 Law of Sines (25)Use the Law of Sines to solve oblique trianglesUse the Law of Sines to solve, if possible, the triangle or triangles in the ambiguous caseFind the area of an oblique triangle use the sine functionSolve applications9.7 Law of Cosines (19)Solve application problemsUse the Law of Cosine to solve oblique trianglesCHAPTER 10: Area10.1 Angles: Polygons & Regular Polygon Tessellations (28)Find and use the measures of interior angles of polygonsFind and use the measures of exterior angles of polygonsSolve problems related to the measures of interior and exterior angles of polygonsDetermine whether a tessellation of regular polygons is formedProve theorems related to the measures of interior and exterior angles of polygons10.2 Areas of Triangles and Quadrilaterals (38)Find the areas of squares, rectangles, parallelograms, and trianglesFind the areas of trapezoids, rhombuses, and kitesFind the areas of irregular figuresGeom.G.27Geom.G.3410.3 Areas of Regular Polygons (29)Find the measures of angles formed between radii and the apothem in regular polygonsFind areas of regular polygonsFind areas of regular polygons using trigonometric ratiosSolve problems involving geometric constructions or proofsUnderstand the relationships among radii, apothems, side lengths, and areas of regular polygonsGeom.G.1310.4 Perimeters and Areas of Similar Figures (28)Find scale factors and ratios of perimeters and areas of similar figuresFind side lengths, perimeters, and areas of similar figuresSolve application problemsSolve problems involving geometric constructionsComplete statements about similar figuresGeom.G.1810.5 Arc Measure, Circumference, and Arc Lengths of Circles (24)Identify and name semicircles, major arcs, and minor arcsFind measures of central angles and arcsFind circumferences and arc lengthsGeom.G.1Geom.G.23 10.6 Areas of Circles and Sectors (25)Find areas of circles, sectors, and segments of circlesFind radii of circlesSolve problems relating regular polygons and circlesGeom.G.25Geom.G.3410.7 Geometric Probability (29)Use segment models to find the probabilities of eventsUse are models to find the probabilities of eventsGeom.SP.1CHAPTER 11: Surface Area and Volume11.1 Solids and Cross Sections (25)Recognize polyhedra and their partsVisualize cross sections of solidsVisualize solids formed by revolving a region about a lineGeom.G.33Geom.G.3411.2 Surface Areas of Prisms and Cylinders (24)Find the surface area of a prismFind the surface area of a cylinderUse visual representations of prisms to determine informationGeom.G.346.G.47.G.611.3 Surface Areas of Pyramids and Cones (20)Find the surface area of a pyramidFind the surface area of a cone7.G.611.4 Volume of Prisms and Cylinders (24)Find the volume of a prismFind the volume of a cylinderFind the volume of a composite solidsGeom.G.32Geom.G.3411.5 Volume of Pyramids and Cones (20)Find the volume of a pyramidFind the volume of a coneGeom.G.32Geom.G.3411.6 Surface Areas and Volumes of Spheres (28)Find the surface area and volume of a sphereUse a coordinate system to determine the position of points on a sphereGeom.G.32Geom.G.3411.7 Areas and Volumes of Similar Solids (16)Compare and find the areas and volumes of similar solidsGeom.G.34Geom.G.357.G.1CHAPTER 12: Circles and Other Conic Sections12.1 Circle Review and Tangent Lines (27)Review circles and arcsUse properties of a tangent line to a circleSolve problems involving geometric proofs or constructionsGeom.G.2312.2 Chords and Arcs (14)Use congruent chords, arcs, and central anglesUse perpendicular bisectors to chordsSolve problems involving geometric proofs or constructionsGeom.G.2312.3 Inscribed Angles (12)Find measures of inscribed angles and/or intercepted arcsFind measures of angles and/or arcs formed by tangent and chordsSolve problems involving geometric proofs or constructionsGeom.G.23Geom.G.2412.4 Additional Angle Measure and Segment Lengths (17)Find measures of angles formed by chords, secants, and tangentsFind the lengths of segments associated with circlesSolve application problemsSolve problems involving geometric proofsGeom.G.2312.5 Circles in the Coordinate Plane (15)Write an equation of a circleFind the center and radius of a circle written in standard formComplete the square to find the center and radius of a circleFind quantities related to circlesFind the points of intersection of pairs of graphsGeom.G.2612.6 Locus (15)Draw and describe lociSolve application problemsGeom.G.36Louisiana Mathematics Standards for Geometry that are not reflected in MyMathLab course exercises:CCSS#Standard DescriptionCommentGeom.G.3Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.Not included in the course.Geom.G.7Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.Requires paper and pencil work.Geom.G.8Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.Requires paper and pencil work.Geom.G.16Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.Requires paper and pencil work.Geom.G.22Prove that all circles are similar.Requires paper and pencil work.Geom.G.31Give an informal argument, e.g., dissection arguments, Cavalieri’s principle, or informal limit arguments. for the formulas for the circumference of a circle; area of a circle; volume of a cylinder, pyramid, and cone. Requires paper and pencil work.Geom.SP.2Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.Not included in the course.Geom.SP.3Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.Not included in the course.Geom.SP.4Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. Not included in the course.Geom.SP.5Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.Not included in the course.Geom.SP.6Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A, and interpret the answer in terms of the model.Not included in the course.Geom.SP.7Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret the answer in terms of the model.Not included in the course. ................
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