# Virginia State Standards Alignment: 9-12

## This alignment shows the Media4Math resources that support the standards shown below. Click on a course to see the Virginia Standards for that course. Then click on a specific standard to see all the Media4Math resources that support it.

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## Algebra 1 | ## Algebra 2 | ## Geometry | ## Trigonometry |

## Algebra 1

A.EO.1 | The student will represent verbal quantitative situations algebraically and evaluate these expressions for given replacement values of the variables. |

A.EO.1.a | Translate between verbal quantitative situations and algebraic expressions, including contextual situations. |

A.EO.1.b | Evaluate algebraic expressions which include absolute value, square roots, and cube roots for given replacement values to include rational numbers, without rationalizing the denominator. |

A.EO.2 | The student will perform operations on and factor polynomial expressions in one variable. |

A.EO.2.a | Determine sums and differences of polynomial expressions in one variable, using a variety of strategies, including concrete objects and their related pictorial and symbolic models. |

A.EO.2.b | Determine the product of polynomial expressions in one variable, using a variety of strategies, including concrete objects and their related pictorial and symbolic models, the application of the distributive property, and the use of area models. The factors should be limited to five or fewer terms (e.g., (4x + 2)(3x + 5) represents four terms and (x + 1)(2x2 + x + 3) represents five terms). |

A.EO.2.c | Factor completely first- and second-degree polynomials in one variable with integral coefficients. After factoring out the greatest common factor (GCF), leading coefficients should have no more than four factors. |

A.EO.2.d | Determine the quotient of polynomials, using a monomial or binomial divisor, or a completely factored divisor. |

A.EO.2.e | Represent and demonstrate equality of quadratic expressions in different forms (e.g., concrete, verbal, symbolic, and graphical). |

A.EO.3 | The student will derive and apply the laws of exponents. |

A.EO.3.a | Derive the laws of exponents through explorations of patterns, to include products, quotients, and powers of bases. |

A.EO.3.b | Simplify multivariable expressions and ratios of monomial expressions in which the exponents are integers, using the laws of exponents. |

A.EO.4 | The student will simplify and determine equivalent radical expressions involving square roots of whole numbers and cube roots of integers. |

A.EO.4.a | Simplify and determine equivalent radical expressions involving the square root of a whole number in simplest form. |

A.EO.4.b | Simplify and determine equivalent radical expressions involving the cube root of an integer. |

A.EO.4.c | Add, subtract, and multiply radicals, limited to numeric square and cube root expressions. |

A.EO.4.d | Generate equivalent numerical expressions and justify their equivalency for radicals using rational exponents, limited to rational exponents of 1/2 and 1/3 (e.g., √5 = 5^(1/2); _8=8^(1/3) = (2^3 )^(1/3) = 2). |

A.EI.1 | The student will represent, solve, explain, and interpret the solution to multistep linear equations and inequalities in one variable and literal equations for a specified variable. |

A.EI.1.a | Write a linear equation or inequality in one variable to represent a contextual situation. |

A.EI.1.b | Solve multistep linear equations in one variable, including those in contextual situations, by applying the properties of real numbers and/or properties of equality. |

A.EI.1.c | Solve multistep linear inequalities in one variable algebraically and graph the solution set on a number line, including those in contextual situations, by applying the properties of real numbers and/or properties of inequality. |

A.EI.1.d | Rearrange a formula or literal equation to solve for a specified variable by applying the properties of equality. |

A.EI.1.e | Determine if a linear equation in one variable has one solution, no solution, or an infinite number of solutions. |

A.EI.1.f | Verify possible solution(s) to multistep linear equations and inequalities in one variable algebraically, graphically, and with technology to justify the reasonableness of the answer(s). Explain the solution method and interpret solutions for problems given in context. |

A.EI.2 | The student will represent, solve, explain, and interpret the solution to a system of two linear equations, a linear inequality in two variables, or a system of two linear inequalities in two variables. |

A.EI.2.a | Create a system of two linear equations in two variables to represent a contextual situation. |

A.EI.2.b | Apply the properties of real numbers and/or properties of equality to solve a system of two linear equations in two variables, algebraically and graphically. |

A.EI.2.c | Determine whether a system of two linear equations has one solution, no solution, or an infinite number of solutions. |

A.EI.2.d | Create a linear inequality in two variables to represent a contextual situation. |

A.EI.2.e | Represent the solution of a linear inequality in two variables graphically on a coordinate plane. |

A.EI.2.f | Create a system of two linear inequalities in two variables to represent a contextual situation. |

A.EI.2.g | Represent the solution set of a system of two linear inequalities in two variables, graphically on a coordinate plane. |

A.EI.2.h | Verify possible solution(s) to a system of two linear equations, a linear inequality in two variable, or a system of two linear inequalities algebraically, graphically, and with technology to justify the reasonableness of the answer(s). Explain the solution method and interpret solutions for problems given in context. |

A.EI.3 | The student will represent, solve, and interpret the solution to a quadratic equation in one variable. |

A.EI.3.a | Solve a quadratic equation in one variable over the set of real numbers with rational or irrational solutions, including those that can be used to solve contextual problems. |

A.EI.3.b | Determine and justify if a quadratic equation in one variable has no real solutions, one real solution, or two real solutions. |

A.EI.3.c | Verify possible solution(s) to a quadratic equation in one variable algebraically, graphically, and with technology to justify the reasonableness of answer(s). Explain the solution method and interpret solutions for problems given in context. |

A.F.1 | The student will investigate, analyze, and compare linear functions algebraically and graphically, and model linear relationships. |

A.F.1.a | Determine and identify the domain, range, zeros, slope, and intercepts of a linear function, presented algebraically or graphically, including the interpretation of these characteristics in contextual situations. |

A.F.1.b | Investigate and explain how transformations to the parent function y = x affects the rate of change (slope) and the y-intercept of a linear function. |

A.F.1.c | Write equivalent algebraic forms of linear functions, including slope-intercept form, standard form, and point-slope form, and analyze and interpret the information revealed by each form. |

A.F.1.d | Write the equation of a linear function to model a linear relationship between two quantities, including those that can represent contextual situations. Writing the equation of a linear function will include the following situations: i) given the graph of a line; ii) given two points on the line whose coordinates are integers; iii) given the slope and a point on the line whose coordinates are integers; |

A.F.1.e | Write the equation of a line parallel or perpendicular to a given line through a given point. |

A.F.1.f | Graph a linear function in two variables, with and without the use of technology, including those that can represent contextual situations. |

A.F.1.g | For any value, x, in the domain of f, determine f(x), and determine x given any value f(x) in the range of f, given an algebraic or graphical representation of a linear function. |

A.F.1.h | Compare and contrast the characteristics of linear functions represented algebraically, graphically, in tables, and in contextual situations. |

A.F.2 | The student will investigate, analyze, and compare characteristics of functions, including quadratic, and exponential functions, and model quadratic and exponential relationships. |

A.F.2.a | Determine whether a relation, represented by a set of ordered pairs, a table, a mapping, or a graph is a function; for relations that are functions, determine the domain and range. |

A.F.2.b | Given an equation or graph, determine key characteristics of a quadratic function including x-intercepts (zeros), y-intercept, vertex (maximum or minimum), and domain and range (including when restricted by context); interpret key characteristics as related to contextual situations, where applicable. |

A.F.2.c | Graph a quadratic function, f(x), in two variables using a variety of strategies, including transformations f(x) + k and kf(x), where k is limited to rational values. |

A.F.2.d | Make connections between the algebraic (standard and factored forms) and graphical representation of a quadratic function. |

A.F.2.e | Given an equation or graph of an exponential function in the form y = abx (where b is limited to a natural number), interpret key characteristics, including y-intercepts and domain and range; interpret key characteristics as related to contextual situations, where applicable. |

A.F.2.f | Graph an exponential function, f(x), in two variables using a variety of strategies, including transformations f(x) + k and kf(x), where k is limited to rational values. |

A.F.2.g | For any value, x, in the domain of f, determine f(x) of a quadratic or exponential function. Determine x given any value f(x) in the range of f of a quadratic function. Explain the meaning of x and f(x) in context. |

A.F.2.h | Compare and contrast the key characteristics of linear functions (f(x) = x), quadratic functions (f(x) = x2), and exponential functions (f(x) = bx) using tables and graphs. |

A.ST.1 | The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and analyze data and communicate results) with a focus on representing bivariate data in scatterplots and determining the curve of best fit using linear and quadratic functions. |

A.ST.1.a | Formulate investigative questions that require the collection or acquisition of bivariate data. |

A.ST.1.b | Determine what variables could be used to explain a given contextual problem or situation or answer investigative questions. |

A.ST.1.c | Determine an appropriate method to collect a representative sample, which could include a simple random sample, to answer an investigative question. |

A.ST.1.d | Given a table of ordered pairs or a scatterplot representing no more than 30 data points, use available technology to determine whether a linear or quadratic function would represent the relationship, and if so, determine the equation of the curve of best fit. |

A.ST.1.e | Use linear and quadratic regression methods available through technology to write a linear or quadratic function that represents the data where appropriate and describe the strengths and weaknesses of the model. |

A.ST.1.f | Use a linear model to predict outcomes and evaluate the strength and validity of these predictions, including through the use of technology. |

A.ST.1.g | Investigate and explain the meaning of the rate of change (slope) and y-intercept (constant term) of a linear model in context. |

A.ST.1.h | Analyze relationships between two quantitative variables revealed in a scatterplot. |

A.ST.1.i | Make conclusions based on the analysis of a set of bivariate data and communicate the results. |

## Algebra 2

A2.EO.1 | The student will perform operations on and simplify rational expressions. |

A2.EO.1.a | Add, subtract, multiply, or divide rational algebraic expressions, simplifying the result. |

A2.EO.1.b | Justify and determine equivalent rational algebraic expressions with monomial and binomial factors. Algebraic expressions should be limited to linear and quadratic expressions. |

A2.EO.1.c | Recognize a complex algebraic fraction and simplify it as a product or quotient of simple algebraic fractions. |

A2.EO.1.d | Represent and demonstrate equivalence of rational expressions written in different forms. |

A2.EO.2 | The student will perform operations on and simplify radical expressions. |

A2.EO.2.a | Simplify and determine equivalent radical expressions that include numeric and algebraic radicands. |

A2.EO.2.b | Add, subtract, multiply, and divide radical expressions that include numeric and algebraic radicands, simplifying the result. Simplification may include rationalizing the denominator. |

A2.EO.2.c | Convert between radical expressions and expressions containing rational exponents. |

A2.EO.3 | The student will perform operations on polynomial expressions in two or more variables and factor polynomial expressions in one and two variables. |

A2.EO.3.a | Determine sums, differences, and products of polynomials in one and two variables. |

A2.EO.3.b | Factor polynomials completely in one and two variables with no more than four terms over the set of integers. |

A2.EO.3.c | Determine the quotient of polynomials in two or more variables, using monomial, binomial, and factorable trinomial divisors. |

A2.EO.3.d | Represent and demonstrate equality of polynomial expressions written in different forms and verify polynomial identities including the difference of squares, sum and difference of cubes, and perfect square trinomials. |

A2.EO.4 | The student will perform operations on complex numbers. |

A2.EO.4.a | Explain the meaning of i. |

A2.EO.4.b | Identify equivalent radical expressions containing negative rational numbers and expressions in a + bi form. |

A2.EO.4.c | Apply properties to add, subtract, and multiply complex numbers. |

A2.EI.1 | The student will represent, solve, and interpret the solution to absolute value equations and inequalities in one variable. |

A2.EI.1.a | Create an absolute value equation in one variable to model a contextual situation. |

A2.EI.1.b | Solve an absolute value equation in one variable algebraically and verify the solution graphically. |

A2.EI.1.c | Create an absolute value inequality in one variable to model a contextual situation. |

A2.EI.1.d | Solve an absolute value inequality in one variable and represent the solution set using set notation, interval notation, and using a number line. |

A2.EI.1.e | Verify possible solution(s) to absolute value equations and inequalities in one variable algebraically, graphically, and with technology to justify the reasonableness of answer(s). Explain the solution method and interpret solutions for problems given in context. |

A2.EI.2 | The student will represent, solve, and interpret the solution to quadratic equations in one variable over the set of complex numbers and solve quadratic inequalities in one variable. |

A2.EI.2.a | Create a quadratic equation or inequality in one variable to model a contextual situation. |

A2.EI.2.b | Solve a quadratic equation in one variable over the set of complex numbers algebraically. |

A2.EI.2.c | Determine the solution to a quadratic inequality in one variable over the set of real numbers algebraically. |

A2.EI.2.d | Verify possible solution(s) to quadratic equations or inequalities in one variable algebraically, graphically, and with technology to justify the reasonableness of answer(s). Explain the solution method and interpret solutions for problems given in context. |

A2.EI.3 | The student will solve a system of equations in two variables containing a quadratic expression. |

A2.EI.3.a | Create a linear-quadratic or quadratic-quadratic system of equations to model a contextual situation. |

A2.EI.3.b | Determine the number of solutions to a linear-quadratic and quadratic-quadratic system of equations in two variables. |

A2.EI.3.c | Solve a linear-quadratic and quadratic-quadratic system of equations algebraically and graphically, including situations in context. |

A2.EI.3.d | Verify possible solution(s) to linear-quadratic or quadratic-quadratic system of equations algebraically, graphically, and with technology to justify the reasonableness of answer(s). Explain the solution method and interpret solutions for problems given in context. |

A2.EI.4 | The student will represent, solve, and interpret the solution to an equation containing rational algebraic expressions. |

A2.EI.4.a | Create an equation containing a rational expression to model a contextual situation. |

A2.EI.4.b | Solve rational equations with real solutions containing factorable algebraic expressions algebraically and graphically. Algebraic expressions should be limited to linear and quadratic expressions. |

A2.EI.4.c | Verify possible solution(s) to rational equations algebraically, graphically, and with technology to justify the reasonableness of answer(s). Explain the solution method and interpret solutions for problems given in context. |

A2.EI.4.d | Justify why a possible solution to an equation containing a rational expression might be extraneous. |

A2.EI.5 | The student will represent, solve, and interpret the solution to an equation containing a radical expression. |

A2.EI.5.a | Solve an equation containing no more than one radical expression algebraically and graphically. |

A2.EI.5.b | Verify possible solution(s) to radical equations algebraically, graphically, and with technology, to justify the reasonableness of answer(s). Explain the solution method and interpret solutions for problems given in context. |

A2.EI.5.c | Justify why a possible solution to an equation with a square root might be extraneous. |

A2.EI.6 | The student will represent, solve, and interpret the solution to a polynomial equation. |

A2.EI.6.a | Determine a factored form of a polynomial equation, of degree three or higher, given its zeros or the x-intercepts of the graph of its related function. |

A2.EI.6.b | Determine the number and type of solutions (real or imaginary) of a polynomial equation of degree three or higher. |

A2.EI.6.c | Solve a polynomial equation over the set of complex numbers. |

A2.EI.6.d | Verify possible solution(s) to polynomial equations of degree three or higher algebraically, graphically, and with technology to justify the reasonableness of answer(s). Explain the solution method and interpret solutions in context. |

A2.F.1 | The student will investigate, analyze, and compare square root, cube root, rational, exponential, and logarithmic function families, algebraically and graphically, using transformations. |

A2.F.1.a | Distinguish between the graphs of parent functions for square root, cube root, rational, exponential, and logarithmic function families. |

A2.F.1.b | b) Write the equation of a square root, cube root, rational, exponential, and logarithmic function, given a graph, using transformations of the parent function, including f(x) + k; f(kx); f(x + k); and kf(x), where k is limited to rational values. Transformations of exponential and logarithmic functions, given a graph, should be limited to a single transformation. |

A2.F.1.c | Graph a square root, cube root, rational, exponential, and logarithmic function, given the equation, using transformations of the parent function including f(x) + k; f(kx); f(x + k); and kf(x), where k is limited to rational values. Use technology to verify transformations of the functions. |

A2.F.1.d | Determine when two variables are directly proportional, inversely proportional, or neither, given a table of values. Write an equation and create a graph to represent a direct or inverse variation, including situations in context. |

A2.F.1.e | Compare and contrast the graphs, tables, and equations of square root, cube root, rational, exponential, and logarithmic functions. |

A2.F.2 | The student will investigate and analyze characteristics of square root, cube root, rational, polynomial, exponential, logarithmic, and piecewise-defined functions algebraically and graphically. |

A2.F.2.a | Determine and identify the domain, range, zeros, and intercepts of a function presented algebraically or graphically, including graphs with discontinuities. |

A2.F.2.b | Compare and contrast the characteristics of square root, cube root, rational, polynomial, exponential, logarithmic, and piecewise-defined functions. |

A2.F.2.c | Determine the intervals on which the graph of a function is increasing, decreasing, or constant. |

A2.F.2.d | Determine the location and value of absolute (global) maxima and absolute (global) minima of a function. |

A2.F.2.e | Determine the location and value of relative (local) maxima or relative (local) minima of a function. |

A2.F.2.f | For any value, x, in the domain of f, determine f(x) using a graph or equation. Explain the meaning of x and f(x) in context, where applicable. |

A2.F.2.g | Describe the end behavior of a function. |

A2.F.2.h | Determine the equations of any vertical and horizontal asymptotes of a function using a graph or equation (rational, exponential, and logarithmic). |

A2.F.2.i | Determine the inverse of a function algebraically and graphically, given the equation of a linear or quadratic function (linear, quadratic, and square root). Justify and explain why two functions are inverses of each other. |

A2.F.2.j | Graph the inverse of a function as a reflection over the line y = x. |

A2.F.2.k | Determine the composition of two functions algebraically and graphically. |

A2.ST.1 | The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and analyze data and communicate results) with a focus on univariate quantitative data represented by a smooth curve, including a normal curve. |

A2.ST.1.a | Formulate investigative questions that require the collection or acquisition of a large set of univariate quantitative data or summary statistics of a large set of univariate quantitative data and investigate questions using a data cycle. |

A2.ST.1.b | Collect or acquire univariate data through research, or using surveys, observations, scientific experiments, polls, or questionnaires. |

A2.ST.1.c | Examine the shape of a data set (skewed versus symmetric) that can be represented by a histogram, and sketch a smooth curve to model the distribution. |

A2.ST.1.d | Identify the properties of a normal distribution. |

A2.ST.1.e | Describe and interpret a data distribution represented by a smooth curve by analyzing measures of center, measures of spread, and shape of the curve. |

A2.ST.1.f | Calculate and interpret the z-score for a value in a data set. |

A2.ST.1.g | Compare two data points from two different distributions using z-scores. |

A2.ST.1.h | Determine the solution to problems involving the relationship of the mean, standard deviation, and z-score of a data set represented by a smooth or normal curve. |

A2.ST.1.i | Apply the Empirical Rule to answer investigative questions. |

A2.ST.1.j | Compare multiple data distributions using measures of center, measures of spread, and shape of the distributions. |

A2.ST.2 | The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and analyze data and communicate results) with a focus on representing bivariate data in scatterplots and determining the curve of best fit using linear, quadratic, exponential, or a combination of these functions. |

A2.ST.2.a | Formulate investigative questions that require the collection or acquisition of bivariate data and investigate questions using a data cycle. |

A2.ST.2.b | Collect or acquire bivariate data through research, or using surveys, observations, scientific experiments, polls, or questionnaires. |

A2.ST.2.c | Represent bivariate data with a scatterplot using technology. |

A2.ST.2.d | Determine whether the relationship between two quantitative variables is best approximated by a linear, quadratic, exponential, or a combination of these functions. |

A2.ST.2.e | Determine the equation(s) of the function(s) that best models the relationship between two variables using technology. Curves of best fit may include a combination of linear, quadratic, or exponential (piecewise-defined) functions. |

A2.ST.2.f | Use the correlation coefficient to designate the goodness of fit of a linear function using technology. |

A2.ST.2.g | Make predictions, decisions, and critical judgments using data, scatterplots, or the equation(s) of the mathematical model. |

A2.ST.2.h | Evaluate the reasonableness of a mathematical model of a contextual situation. |

A2.ST.3 | The student will compute and distinguish between permutations and combinations. |

A2.ST.3.a | Compare and contrast permutations and combinations to count the number of ways that events can occur. |

A2.ST.3.b | Calculate the number of permutations of n objects taken r at a time. |

A2.ST.3.c | Calculate the number of combinations of n objects taken r at a time. |

A2.ST.3.d | Use permutations and combinations as counting techniques to solve contextual problems. |

A2.ST.3.e | Calculate and verify permutations and combinations using technology. |

## Geometry

G.RLT.1 | The student will translate logic statements, identify conditional statements, and use and interpret Venn diagrams. |

G.RLT.1.a | Translate propositional statements and compound statements into symbolic form, including negations (~p, read "not p"), conjunctions (p ∧ q, read "p and q"), disjunctions (p ∨ q, read "p or q"), conditionals (p → q, read "if p then q"), and biconditionals (p ↔ q, read "p if and only if q"), including statements representing geometric relationships. |

G.RLT.1.b | Identify and determine the validity of the converse, inverse, and contrapositive of a conditional statement, and recognize the connection between a biconditional statement and a true conditional statement with a true converse, including statements representing geometric relationships. |

G.RLT.1.c | Use Venn diagrams to represent set relationships, including union, intersection, subset, and negation. |

G.RLT.1.d | Interpret Venn diagrams, including those representing contextual situations. |

G.RLT.2 | The student will analyze, prove, and justify the relationships of parallel lines cut by a transversal. |

G.RLT.2.a | Prove and justify angle pair relationships formed by two parallel lines and a transversal, including: i) corresponding angles; ii) alternate interior angles; iii) alternate exterior angles; iv) same-side (consecutive) interior angles; and v) same-side (consecutive) exterior angles. |

G.RLT.2.b | Prove two or more lines are parallel given angle measurements expressed numerically or algebraically. |

G.RLT.2.c | Solve problems by using the relationships between pairs of angles formed by the intersection of two parallel lines and a transversal. |

G.RLT.3 | The student will solve problems, including contextual problems, involving symmetry and transformation. |

G.RLT.3.a | Locate, count, and draw lines of symmetry given a figure, including figures in context. |

G.RLT.3.b | Determine whether a figure has point symmetry, line symmetry, both, or neither, including figures in context. |

G.RLT.3.c | Given an image or preimage, identify the transformation or combination of transformations that has/have occurred. Transformations include: i) translations; ii) reflections over any horizontal or vertical line or the lines y = x or y = -x; iii) clockwise or counterclockwise rotations of 90°, 180°, 270°, or 360° on a coordinate grid where the center of rotation is limited to the origin; and iv) dilations, from a fixed point on a coordinate grid. |

G.TR.1 | The student will determine the relationships between the measures of angles and lengths of sides in triangles, including problems in context. |

G.TR.1.a | Given the lengths of three segments, determine whether a triangle could be formed. |

G.TR.1.b | Given the lengths of two sides of a triangle, determine the range in which the length of the third side must lie. |

G.TR.1.c | Order the sides of a triangle by their lengths when given information about the measures of the angles. |

G.TR.1.d | Order the angles of a triangle by their measures when given information about the lengths of the sides. |

G.TR.1.e | Solve for interior and exterior angles of a triangle, when given two angles. |

G.TR.2 | The student will, given information in the form of a figure or statement, prove and justify two triangles are congruent using direct and indirect proofs, and solve problems involving measured attributes of congruent triangles. |

G.TR.2.a | Use definitions, postulates, and theorems (including Side-Side-Side (SSS); Side-Angle-Side (SAS); Angle-Side-Angle (ASA); Angle-Angle-Side (AAS); and Hypotenuse-Leg (HL)) to prove and justify two triangles are congruent. |

G.TR.2.b | Use algebraic methods to prove that two triangles are congruent. |

G.TR.2.c | Use coordinate methods, such as the slope formula and the distance formula, to prove two triangles are congruent. |

G.TR.2.d | Given a triangle, use congruent segment, congruent angle, and/or perpendicular line constructions to create a congruent triangle (SSS, SAS, ASA, AAS, and HL). |

G.TR.3 | The student will, given information in the form of a figure or statement, prove and justify two triangles are similar using direct and indirect proofs, and solve problems, including those in context, involving measured attributes of similar triangles. |

G.TR.3.a | Use definitions, postulates, and theorems (including Side-Angle-Side (SAS); Side-Side-Side (SSS); and Angle-Angle (AA)) to prove and justify that triangles are similar. |

G.TR.3.b | Use algebraic methods to prove that triangles are similar. |

G.TR.3.c | Use coordinate methods, such as the slope formula and the distance formula, to prove two triangles are similar. |

G.TR.3.d | Describe a sequence of transformations that can be used to verify similarity of triangles located in the same plane. |

G.TR.3.e | Solve problems, including those in context involving attributes of similar triangles. |

G.TR.4 | The student will model and solve problems, including those in context, involving trigonometry in right triangles and applications of the Pythagorean Theorem. |

G.TR.4.a | Determine whether a triangle formed with three given lengths is a right triangle. |

G.TR.4.b | Find and verify trigonometric ratios using right triangles. |

G.TR.4.c | Model and solve problems, including those in context, involving right triangle trigonometry (sine, cosine, and tangent ratios). |

G.TR.4.d | Solve problems using the properties of special right triangles. |

G.TR.4.e | Solve for missing lengths in geometric figures, using properties of 45°-45°-90° triangles, where rationalizing denominators may be necessary. |

G.TR.4.f | Solve for missing lengths in geometric figures, using properties of 30°-60°-90° triangles, where rationalizing denominators may be necessary. |

G.TR.4.g | Solve problems, including those in context, involving right triangles using the Pythagorean Theorem and its converse, including recognizing Pythagorean Triples. |

G.PC.1 | The student will prove and justify theorems and properties of quadrilaterals, and verify and use properties of quadrilaterals to solve problems, including the relationships between the sides, angles, and diagonals. |

G.PC.1.a | Solve problems, using the properties specific to parallelograms, rectangles, rhombi, squares, isosceles trapezoids, and trapezoids. |

G.PC.1.b | Prove and justify that quadrilaterals have specific properties, using coordinate and algebraic methods, such as the slope formula, the distance formula, and the midpoint formula. |

G.PC.1.c | Prove and justify theorems and properties of quadrilaterals using deductive reasoning. |

G.PC.1.d | Use congruent segment, congruent angle, angle bisector, perpendicular line, and/or parallel line constructions to verify properties of quadrilaterals. |

G.PC.2 | The student will verify relationships and solve problems involving the number of sides and angles of convex polygons. |

G.PC.2.a | Solve problems involving the number of sides of a regular polygon given the measures of the interior and exterior angles of the polygon. |

G.PC.2.b | Justify the relationship between the sum of the measures of the interior and exterior angles of a convex polygon and solve problems involving the sum of the measures of the angles. |

G.PC.2.c | Justify the relationship between the measure of each interior and exterior angle of a regular polygon and solve problems involving the measures of the angles. |

G.PC.3 | The student will solve problems, including those in context, by applying properties of circles. |

G.PC.3.a | Determine the proportional relationship between the arc length or area of a sector and other parts of a circle. |

G.PC.3.b | Solve for arc measures and angles in a circle formed by central angles. |

G.PC.3.c | Solve for arc measures and angles in a circle involving inscribed angles. |

G.PC.3.d | Calculate the length of an arc of a circle. |

G.PC.3.e | Calculate the area of a sector of a circle. |

G.PC.3.f | Apply arc length or sector area to solve for an unknown measurement of the circle including the radius, diameter, arc measure, central angle, arc length, or sector area. |

G.PC.4 | The student will solve problems in the coordinate plane involving equations of circles. |

G.PC.4.a | Derive the equation of a circle of given the center and radius using the Pythagorean Theorem. |

G.PC.4.b | Solve problems in the coordinate plane involving equations of circles: i) given a graph or the equation of a circle in standard form, identify the coordinates of the center of the circle; ii) given the coordinates of the endpoints of a diameter of a circle, determine the coordinates of the center of the circle. iii) given a graph or the equation of a circle in standard form, identify the length of the radius or diameter of the circle. iv) given the coordinates of the endpoints of the diameter of a circle, determine the length of the radius or diameter of the circle. v) given the coordinates of the center and the coordinates of a point on the circle, determine the length of the radius or diameter of the circle; and vi) given the coordinates of the center and length of the radius of a circle, identify the coordinates of a point(s) on the circle. |

G.PC.4.c | Determine the equation of a circle given: i) a graph of a circle with a center with coordinates that are integers; ii) coordinates of the center and a point on the circle; iii) coordinates of the center and the length of the radius or diameter; and iv) coordinates of the endpoints of a diameter. |

G.DF.1 | The student will create models and solve problems, including those in context, involving surface area and volume of rectangular and triangular prisms, cylinders, cones, pyramids, and spheres. |

G.DF.1.a | Identify the shape of a two-dimensional cross section of a three-dimensional figure. |

G.DF.1.b | Create models and solve problems, including those in context, involving surface area of three-dimensional figures, as well as composite three-dimensional figures. |

G.DF.1.c | Solve multistep problems, including those in context, involving volume of three-dimensional figures, as well as composite three-dimensional figures. |

G.DF.1.d | Determine unknown measurements of three-dimensional figures using information such as length of a side, area of a face, or volume. |

G.DF.2 | The student will determine the effect of changing one or more dimensions of a three-dimensional geometric figure and describe the relationship between the original and changed figure. |

G.DF.2.a | Describe how changes in one or more dimensions of a figure affect other derived measures (perimeter, area, total surface area, and volume) of the figure. |

G.DF.2.b | Describe how changes in surface area and/or volume of a figure affect the measures of one or more dimensions of the figure. |

G.DF.2.c | Solve problems, including those in context, involving changing the dimensions or derived measures of a three-dimensional figure. |

G.DF.2.d | Compare ratios between side lengths, perimeters, areas, and volumes of similar figures. |

G.DF.2.e | Recognize when two- and three-dimensional figures are similar and solve problems, including those in context, involving attributes of similar geometric figures. |

## Trigonometry

T.TT.1 | The student will determine the sine, cosine, tangent, cotangent, secant, and cosecant of the acute angles in a right triangle and use these ratios to solve for missing sides and angle measures, including application in contextual problems. |

T.TT.1.a | Define and represent the six triangular trigonometric ratios (sine, cosine, tangent, cosecant, secant, and cotangent) of an angle in a right triangle. |

T.TT.1.b | Describe the relationships between side lengths in special right triangles (30°-60°-90° and 45°-45°-90°). |

T.TT.1.c | Use the trigonometric functions, the Pythagorean Theorem, the Law of Sines, and the Law of Cosines to solve contextual problems. |

T.TT.1.d | Represent and solve contextual problems involving right triangles, including problems involving angles of elevation and depression. |

T.TT.2 | The student will find the area of any triangle and solve for the lengths of the sides and measures of the angles in a non-right triangle using the Law of Sines and the Law of Cosines. |

T.TT.2.a | Apply the Law of Sines, and the Law of Cosines, as appropriate, to find missing sides and angles in non-right triangles. |

T.TT.2.b | Recognize the ambiguous case when applying the Law of Sines and the potential for two triangle solutions in some situations. |

T.TT.2.c | Solve problems that integrate the use of the Law of Sines and the Law of Cosines and the triangle area formula (Area = 1/2absinC, where a and b are triangle sides and C is the included angle) to find the area of any triangle, including those in contextual problems. |

T.CT.1 | The student will determine the degree and radian measure of angles; sketch angles in standard position on a coordinate plane; and determine the sine, cosine, tangent, cosecant, secant, and cotangent of an angle, given a point on the terminal side of an angle in standard position or the value of a trigonometric function of the angle. |

T.CT.1.a | Define a radian as a unit of angle measure and determine the relationship between the radian measure of an angle and the length of the intercepted arc in a circle. |

T.CT.1.b | Determine the degree and radian measure of angles to include both negative and positive rotations in the coordinate plane. |

T.CT.1.c | Find both positive and negative coterminal angles for a given angle. |

T.CT.1.d | Identify the quadrant or axis in/on which the terminal side of an angle lies. |

T.CT.1.e | Draw a reference right triangle when given a point on the terminal side of an angle in standard position. |

T.CT.1.f | Draw a reference right triangle when given the value of a trigonometric function of an angle (sine, cosine, tangent, cosecant, secant, and cotangent). |

T.CT.1.g | Determine the value of any trigonometric function (sine, cosine, tangent, cosecant, secant, and cotangent) when given a point on the terminal side of an angle in standard position. |

T.CT.1.h | Given one trigonometric function value, determine the other five trigonometric function values. |

T.CT.1.i | Calculate the length of an arc of a circle in radians. |

T.CT.1.j | Calculate the area of a sector of a circle. |

T.CT.2 | The student will develop and apply the properties of the unit circle in degrees and radians. |

T.CT.2.a | Convert between radian and degree measure of special angles of the unit circle without the use of technology. |

T.CT.2.b | Define the six circular trigonometric functions of an angle in standard position on the unit circle. |

T.CT.2.c | Apply knowledge of right triangle trigonometry, special right triangles, and the properties of the unit circle to determine trigonometric functions values of special angles (0°, 30°, 45°, 60°, and 90°) and their related angles in degree and radians without the use of technology. |

T.GT.1 | The student will graph and analyze trigonometric functions and apply trigonometric functions to represent periodic phenomena. |

T.GT.1.a | Sketch the graph of the six parent trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent) for at least a two-period interval. |

T.GT.1.b | Determine the domain and range, amplitude, period, and asymptote locations for a trigonometric function, given a graph or an equation. |

T.GT.1.c | Describe the effects of changing the parameters (A, B, C, or D in the standard form of a trigonometric equation) on the graph of the function using graphing technology. |

T.GT.1.d | Sketch the graph of a transformed sine, cosine, and tangent function written in standard form by using transformations for at least a two-period interval, including both positive and negative values for the domain. |

T.GT.1.e | Apply trigonometric functions and their graphs to represent periodic phenomena. |

T.GT.2 | The student will graph the six inverse trigonometric functions. |

T.GT.2.a | Determine the domain and range of the inverse trigonometric functions. |

T.GT.2.b | Use the restrictions on the domain of an inverse trigonometric function to determine a value of the inverse trigonometric function. |

T.GT.2.c | Graph inverse trigonometric functions. |

T.IE.1 | The student will evaluate expressions involving the six trigonometric functions and the inverse sine, cosine, and tangent functions. |

T.IE.1.a | Determine the values of trigonometric functions, with and without graphing technology. |

T.IE.1.b | Determine angle measures by using the inverse trigonometric functions, with and without a graphing technology. |

T.IE.1.c | Evaluate composite functions that involve trigonometric functions and inverse trigonometric functions. |

T.IE.2 | The student will use basic trigonometric identity substitutions to simplify and verify trigonometric identities. |

T.IE.2.a | Use trigonometric identities to make algebraic substitutions to simplify and verify trigonometric identities. The basic trigonometric identities include i) reciprocal identities; ii) Pythagorean identities; iii) sum and difference identities; iv) double-angle identities; and v) half-angle identities. |

T.IE.2.b | Apply the sum, difference, and half-angle identities to evaluate trigonometric function values of angles that are not integer multiples of the special angles to solve problems, including contextual situations. |

T.IE.3 | The student will solve trigonometric equations and inequalities. |

T.IE.3.a | Solve trigonometric equations with and without restricted domains algebraically and graphically. |

T.IE.3.b | Solve trigonometric inequalities algebraically and graphically. |

T.IE.3.c | Verify and justify algebraic solutions to trigonometric equations and inequalities, using graphing technology. |