Geometry
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Geometry
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A.APR.1Arithmetic With Polynomials And Rational ExpressionsPerform Arithmetic Operations On PolynomialsUnderstand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
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G.CO.1CongruenceExperiment With Transformations In The PlaneKnow precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
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G.C.1CirclesUnderstand And Apply Theorems About CirclesProve that all circles are similar.
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G.C.2CirclesUnderstand And Apply Theorems About CirclesIdentify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.
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G.C.3CirclesUnderstand And Apply Theorems About CirclesConstruct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
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G.C.4CirclesUnderstand And Apply Theorems About Circles(+) Construct a tangent line from a point outside a given circle to the circle.
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G.C.5CirclesFind Arc Lengths And Areas Of Sectors Of CirclesDerive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.
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G.CO.10CongruenceProve Geometric TheoremsProve theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
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G.CO.11CongruenceProve Geometric TheoremsProve theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.
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G.CO.12CongruenceMake Geometric ConstructionsMake formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
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G.CO.13CongruenceMake Geometric ConstructionsConstruct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
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G.CO.2CongruenceExperiment With Transformations In The PlaneRepresent transformations in the plane using, e.g. transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g. translation versus horizontal stretch).
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G.CO.3CongruenceExperiment With Transformations In The PlaneGiven a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
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G.CO.4CongruenceExperiment With Transformations In The PlaneDevelop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
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G.CO.5CongruenceExperiment With Transformations In The PlaneGiven a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g. graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
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G.CO.6CongruenceUnderstand Congruence In Terms Of Rigid MotionsUse geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
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G.CO.7CongruenceUnderstand Congruence In Terms Of Rigid MotionsUse 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.
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G.CO.8CongruenceUnderstand Congruence In Terms Of Rigid MotionsExplain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
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G.CO.9CongruenceProve Geometric TheoremsProve theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.
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G.GMD.1Geometric Measurement And DimensionExplain Volume Formulas And Use Them To Solve ProblemsGive an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.
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G.GMD.3Geometric Measurement And DimensionExplain Volume Formulas And Use Them To Solve ProblemsUse volume formulas for cylinders, pyramids, cones, and spheres to solve problems.★
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G.GMD.4Geometric Measurement And DimensionVisualize Relationships Between Two-Dimensional And Three- Dimensional ObjectsIdentify the shapes of two-dimensional cross-sections of three- dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
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G.GPE.1Expressing Geometric Properties With EquationsTranslate Between The Geometric Description And The Equation For A Conic SectionDerive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.
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G.GPE.4Expressing Geometric Properties With EquationsUse Coordinates To Prove Simple Geometric Theorems AlgebraicallyUse coordinates to prove simple geometric theorems algebraically.
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G.GPE.5Expressing Geometric Properties With EquationsUse Coordinates To Prove Simple Geometric Theorems AlgebraicallyProve the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g. find the equation of a line parallel or perpendicular to a given line that passes through a given point).
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G.GPE.6Expressing Geometric Properties With EquationsUse Coordinates To Prove Simple Geometric Theorems AlgebraicallyFind the point on a directed line segment between two given points that partitions the segment in a given ratio.
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G.GPE.7Expressing Geometric Properties With EquationsUse Coordinates To Prove Simple Geometric Theorems AlgebraicallyUse coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g. using the distance formula.★
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G.MG.1Modeling With GeometryApply Geometric Concepts In Modeling SituationsUse geometric shapes, their measures, and their properties to describe objects (e.g. modeling a tree trunk or a human torso as a cylinder).★
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G.MG.2Modeling With GeometryApply Geometric Concepts In Modeling SituationsApply concepts of density based on area and volume in modeling situations (e.g. persons per square mile, BTUs per cubic foot).★
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G.MG.3Modeling With GeometryApply Geometric Concepts In Modeling SituationsApply geometric methods to solve design problems (e.g. designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).★
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G.SRT.1Similarity, Right Triangles, And TrigonometryUnderstand Similarity In Terms Of Similarity TransformationsVerify experimentally the properties of dilations given by a center and a scale factor:
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G.SRT.1.aSimilarity, Right Triangles, And TrigonometryUnderstand Similarity In Terms Of Similarity TransformationsA dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
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G.SRT.1.bSimilarity, Right Triangles, And TrigonometryUnderstand Similarity In Terms Of Similarity TransformationsThe dilation of a line segment is longer or shorter in the ratio given by the scale factor.
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G.SRT.11Similarity, Right Triangles, And TrigonometryApply Trigonometry To General Triangles(+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g. surveying problems, resultant forces).
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G.SRT.2Similarity, Right Triangles, And TrigonometryUnderstand Similarity In Terms Of Similarity TransformationsGiven two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
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G.SRT.3Similarity, Right Triangles, And TrigonometryUnderstand Similarity In Terms Of Similarity TransformationsUse the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
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G.SRT.4Similarity, Right Triangles, And TrigonometryProve Theorems Involving SimilarityProve theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.
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G.SRT.5Similarity, Right Triangles, And TrigonometryProve Theorems Involving SimilarityUse congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
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G.SRT.6Similarity, Right Triangles, And TrigonometryDefine Trigonometric Ratios And Solve Problems Involving Right TrianglesUnderstand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
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G.SRT.7Similarity, Right Triangles, And TrigonometryDefine Trigonometric Ratios And Solve Problems Involving Right TrianglesExplain and use the relationship between the sine and cosine of complementary angles.
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G.SRT.8Similarity, Right Triangles, And TrigonometryDefine Trigonometric Ratios And Solve Problems Involving Right TrianglesUse trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.★
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S.CP.2Conditional Probability And The Rules Of ProbabilityUnderstand Independence And Conditional Probability And Use Them To Interpret DataUnderstand 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.
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S.CP.5Conditional Probability And The Rules Of ProbabilityUnderstand Independence And Conditional Probability And Use Them To Interpret DataRecognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.
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