Prentice Hall Mathematics: Geometry 2007 Correlated to: Arizona Academic Standards for Mathematics (Grades 9-12)

Transcription

1 Strand 1: Number Sense and Operations Every student should understand and use all concepts and skills from the previous grade levels. The standards are designed so that new learning builds on preceding skills and are needed to learn new skills. Communication, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of mathematical strands. Concept 1: Number Sense Understand and apply numbers, ways of representing numbers, the relationships among numbers and different number systems. PO 1. Classify real numbers as members of one or more subsets: natural, whole, integers, rational, or Algebra 1 and referenced on page 767. irrational numbers PO 2. Identify properties of the real number system: commutative, associative, distributive, identity, inverse, and closure. Algebra 1 and Algebra 2. PO 3. Distinguish between finite and infinite sets of numbers. Algebra 1 and Algebra 2. Concept 2: Numerical Operations Understand and apply numerical operations and their relationship to one another. PO 1. Select the grade-level appropriate operation SE/TE: 60, 405, 424, 451, 552, 615 to solve word problems PO 2. Solve word problems using grade-level appropriate operations and numbers SE/TE: 60, 405, 424, 451, 552, 615 PO 3. Simplify numerical expressions including signed numbers and absolute values Algebra 1 and Algebra 2 plus referenced on pages 754, 757 1

2 PO 4. Apply subscripts to represent ordinal position Algebra 1 PO 5. Use grade level-appropriate mathematical terminology SE/TE: 30, , 130, 165, 234, 288, , , , , 372, 504, 524, 574, 607, 759 TE: 106, 107, 131, 294, 350, 352, 368, 370 PO 6. Compute using scientific notation PO 7. Simplify numerical expressions using the order of operations. Concept 3: Estimation Use estimation strategies reasonably and fluently. PO 1. Solve grade-level appropriate problems using estimation Algebra 1 Algebra 1 and Algebra 2 SE/TE: 41, 66, 206, 549, 557, 581, 612, 627, 706 TE: 40, 42, 63, 207, 208, 613, 629 web code: aua-0106, aue-0106, aua-1003, aue- 1003, aue-1004, aua-1004, aue-01102, aua-1102 PO 2. Determine if a solution to a problem is reasonable Algebra 1 and referenced in Algebra 2. This is also referenced in this text on page 748 PO 3. Determine rational approximations of irrational numbers. Algebra 1 and Algebra 2 2

3 Strand 2: Data Analysis, Probability, and Discrete Mathematics Every student should understand and use all concepts and skills from the previous grade levels. The standards are designed so that new learning builds on preceding skills and are needed to learn new skills. Communication, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of mathematical strands. Concept 1: Data Analysis (Statistics) Understand and apply data collection, organization and representation to analyze and sort data. PO 1. Formulate questions to collect data in contextual situations PO 2. Organize collected data into an appropriate graphical representation Algebra 1 and Algebra 2 SE/TE: 18, , , 499, 566, 696, 714, 751, 752 TE: 169, 170, 500, 567, 697 PO 3. Display data as lists, tables, matrices, and plots. SE/TE: 18, , , 187, 458, 499, , 524, 563, 566, 696, 714, 742, 751, 752, 763, , 768 TE: 169, 170, 500, 562, 567, 697 web codes: aue-2104, aue-1005, aua-1005 PO 4. Construct equivalent displays of the same data SE/TE: 18, , , 187, 458, 499, , 524, 563, 566, 696, 714, 742, 751, 752, 763, , 768 TE: 169, 170, 500, 562, 567, 697 web codes: aue-2104, aue-1005, aua

4 PO 5. Identify graphic misrepresentations and distortions of sets of data Algebra 1 and Algebra 2 PO 6. Identify which of the measures of central tendency is most appropriate in a given situation SE/TE: 271, 274, 275, 298, 392, 409, 750 TE: 273, 276, 394, 395 web codes PO 7. Make reasonable predictions based upon linear patterns in data sets or scatter plots SE/TE: 76, 175, 492, 524, 751 TE: 176, 177, 493 PO 8. Make reasonable predictions for a set of data, based on patterns SE/TE: 76, 175, 492, 524, 751 TE: 176, 177, 493 PO 9. Draw inferences from charts, tables, graphs, plots, or data sets SE/TE: 5, 6, 18, 27, 49, 69, , , 185, 187, 204, 258, 320, 458, 499, , 524, 563, 566, 696, 714, 742, 751, 752, 763, , 768 TE: 8, 26, 169, 170, 184, 500, 562, 567, 697 4

5 web codes: aua-0104, aue-0104, aue-2104, aua- 0107, aue-0107, aue-0308, aua-0308, aue-1005, aua-1005 PO 10. Apply the concepts of mean, median, SE/TE: 18, , , 187, 458, 499, mode, range, and quartiles to summarize data sets , 524, 563, 566, 567, 696, 714, 742, 751, 752, 763, , 768 TE: 169, 170, 500, 562, 567, 697 web codes: aue-2104, aue-1005, aua-1005 PO 11. Evaluate the reasonableness of conclusions drawn from data analysis SE/TE: 748 PO 12. Recognize and explain the impact of interpreting data (making inferences or drawing conclusions) from a biased sample SE/TE: 5, 6, 18, 27, 49, 69, , , 185, 187, 204, 258, 320, 458, 499, , 524, 563, 566, 696, 714, 742, 751, 752, 763, , 768 TE: 8, 26, 169, 170, 184, 500, 562, 567, 697 web codes: aua-0104, aue-0104, aue-2104, aua- 0107, aue-0107, aue-0308, aua-0308, aue-1005, aua-1005 PO 13. Draw a line of best fit for a scatter plot Algebra 1 and Algebra 2 PO 14. Determine whether displayed data has positive, negative, or no correlation SE/TE: 5, 6, 18, 27, 49, 69, , , 185, 187, 204, 258, 320, 458, 499, , 524, 563, 566, 696, 714, 742, 751, 752, 763, , 768 5

6 TE: 8, 26, 169, 170, 184, 500, 562, 567, 697 web codes: aua-0104, aue-0104, aue-2104, aua- 0107, aue-0107, aue-0308, aua-0308, aue-1005, aua-1005 PO 15. Identify a normal distribution PO 16. Identify differences between sampling and census Algebra 1 and Algebra 2 Algebra 1 and Algebra 2 PO 17. Identify differences between biased and unbiased samples. Algebra 1 and Algebra 2 Concept 2: Probability Understand and apply the basic concepts of probability. PO 1. Find the probability that a specific event will occur, with or without replacement Algebra 2 plus in this text on pages: 582, 583, 584, 591, 762 TE: 585, 586 PO 2. Determine simple probabilities related to geometric figures Algebra 2 plus in this text on pages: 582, 583, 584, 591, 762 TE: 585, 586 PO 3. Predict the outcome of a grade-level appropriate probability experiment Algebra 2 plus in this text on pages: 582, 583, 584, 591, 762 6

7 TE: 585, 586 PO 4. Record the data from performing a gradelevel appropriate probability experiment Algebra 2 plus in this text on pages: 582, 583, 584, 591, 762 TE: 585, 586 PO 5. Compare the outcome of an experiment to predictions made prior to performing the experiment Algebra 2 plus in this text on pages: 582, 583, 584, 591, 762 TE: 585, 586 PO 6. Distinguish between independent and dependent events Algebra 2 plus in this text on pages: 582, 583, 584, 591, 762 TE: 585, 586 PO 7. Compare the results of two repetitions of the same grade-level appropriate probability experiment. Algebra 2 plus in this text on pages: 582, 583, 584, 591, 762 TE: 585, 586 7

8 Concept 3: Discrete Mathematics Systematic Listing and Counting Understand and demonstrate the systematic listing and counting of possible outcomes. PO 1. Determine the number of possible outcomes for a contextual event using a chart, a tree Algebra 2 plus in this text on pages: 582, diagram, or the counting principle 583, 584, 591, 762 TE: 585, 586 PO 2. Determine when to use combinations versus permutations in counting objects Algebra 2 plus in this text on pages: 582, 583, 584, 591, 762 TE: 585, 586 PO 3. Use combinations or permutations to solve contextual problems. Algebra 2 plus in this text on pages: 582, 583, 584, 591, 762 TE: 585, 586 Concept 4: Vertex-Edge Graphs Understand and apply vertex-edge graphs. No standards for high school level. 8

9 Strand 3: Patterns, Algebra, and Functions Every student should understand and use all concepts and skills from the previous grade levels. The standards are designed so that new learning builds on preceding skills and are needed to learn new skills. Communication, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of mathematical strands. Concept 1: Patterns Identify patterns and apply pattern recognition to reason mathematically. PO 1. Communicate a grade-level appropriate iterative or recursive pattern, using symbols or Algebra 2 plus in this text on pages: 3, 12, numbers 72, 378, 514, 584, 585, 609, 631, 653, 656, 742, 768 TE: 586, 612, 613, 632 web codes: aue-1008, auj-1051, aua-1152 PO 2. Find the nth term of an iterative or recursive pattern Algebra 2 plus in this text on pages: 3, 12, 72, 378, 514, 584, 585, 609, 631, 653, 656, 742, 768 TE: 586, 612, 613, 632 web codes: aue-1008, auj-1051, aua-1152 PO 3. Evaluate problems using basic recursion formulas. Algebra 2 Concept 2: Functions and Relationships Describe and model functions and their relationships. PO 1. Determine if a relationship is a function, given a graph, table, or set of ordered pairs Algebra 2 plus in this text on page: 248 PO 2. Describe a contextual situation that is depicted by a given graph SE/TE: 18, , , 499, 566, 696, 714, 751, 752 TE: 169, 170, 500, 567, 697 9

10 PO 3. Identify a graph that models a given realworld situation SE/TE: 6, 18, , , 181, 214, 322, 345, 375, 401, 499, 555, 566, 696, 714, 751, 752 TE: 169, 170, 182, 216, 344, 346, 376, 500, 554, 567, 697 web codes: aua-0606, aue-0606 PO 4. Sketch a graph that models a given contextual situation SE/TE: 18, , , 499, 566, 696, 714, 751, 752 TE: 169, 170, 500, 567, 697 PO 5. Determine domain and range for a function Algebra 1 PO 6. Determine the solution to a contextual maximum/minimum problem, given the graphical representation SE/TE: 18, , , 499, 566, 696, 714, 751, 752 TE: 169, 170, 500, 567, 697 PO 7. Express the relationship between two variables using tables/matrices, equations, or graphs Algebra 2 plus referenced on page:

11 PO 8. Interpret the relationship between data suggested by tables/matrices, equations, or graphs SE/TE: 76-77, 163, , , , 567, , web codes: aua-0305, aue-0305 PO 9. Determine from two linear equations whether the lines are parallel, perpendicular, coincident, or intersecting but not perpendicular. SE/TE: 126, , , , 175, 176, , 190, 507 TE: 139, 143, 144, 169, 177, 179, 184, 185 Concept 3: Algebraic Representations Represent and analyze mathematical situations and structures using algebraic representations. PO 1. Evaluate algebraic expressions, including absolute value and square roots SE/TE: 753, 754, 757, 768 PO 2. Simplify algebraic expressions SE/TE: 753, 754, 757, 768 PO 3. Multiply and divide monomial expressions SE/TE: 753, 754, 757, 768 with integral exponents PO 4. Translate a written expression or sentence into a mathematical expression or sentence SE/TE: 753, 754, 757, 768 PO 5. Translate a sentence written in context into an algebraic equation involving multiple operations SE/TE: 18, 168, 175, 176, 234, 372, 607, , 709, 753, 754, 757, 759, 765, 768 TE: 169, 177, 179, 698,

12 PO 6. Write a linear equation for a table of values SE/TE: , 168, , 175, 176, 187, 191, 234, 563, 742, 760, , 768 TE: 169, 177, 179, 562 web codes: aue-2104, aue-1005, aua-1005 PO 7. Write a linear algebraic sentence that represents a data set that models a contextual situation. SE/TE: , 168, , 175, 176, 187, 191, 234, 563, 742, 760, , 768 TE: 169, 177, 179, 562 web codes: aue-2104, aue-1005, aua-1005 PO 8. Solve linear (first degree) equations in one variable (may include absolute value) SE/TE: , 168, 175, 176, 191, 234, 760, 765 TE: 169, 177, 179 PO 9. Solve linear inequalities in one variable PO 10. Write an equation of the line given: two points on the line, the slope and a point on the line, or the graph of the line Algebra 2 SE/TE: , 168, 175, 176, 191, 234, 760, 765 TE: 169, 177,

13 PO 11. Solve an algebraic proportion SE/TE: , 397, , 407 TE: 370, 401, 403 web codes: auj-0751 PO 12. Solve systems of linear equations in two variables (integral coefficients and rational solutions) SE/TE: 30, , 168, , 175, 191, 234, 758, 760, 765 TE: 169, 177, 179 PO 13. Add, subtract, and perform scalar multiplication with matrices SE/TE: 458, 504, 505, 524 PO 14. Calculate powers and roots of real numbers, both rational and irrational, using technology when appropriate PO 15. Simplify square roots and cube roots with monomial radicands (including those with variables) that are perfect squares or perfect cubes PO 16. Solve square root radical equations involving only one radical SE/TE: 640, 753, 768 SE/TE: 640, 753, 768 SE/TE: 640, 753,

14 PO 17. Solve quadratic equations PO 18. Identify the sine, cosine, and tangent ratios of the acute angles of a right triangle. Algebra 2 plus referenced in this text on page 372 SE/TE: , , 462, 565, 694, 707, 764, 769 TE: 435, 436, 441, 442 Concept 4: Analysis of Change Analyze change in a variable over time and in various contexts. PO 1. Determine slope, x-, and y-intercepts of a SE/TE: 166, 167, 175, 191 linear equation PO 2. Solve formulas for specified variables. TE: 169, 177, 179 web codes Algebra 2 plus referenced in this text on page: 296 Strand 4: Geometry and Measurement Every student should understand and use all concepts and skills from the previous grade levels. The standards are designed so that new learning builds on preceding skills and are needed to learn new skills. Communication, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of mathematical strands. Concept 1: Geometric Properties Analyze the attributes and properties of 2- and 3-dimensional shapes and develop mathematical arguments about their relationships. PO 1. Identify the attributes of special triangles (isosceles, equilateral, right) SE/TE: 148, , 229, 230, , 251, 419, , 427, 429, 549, 581, 764 TE: 150, 221, 232, 238, 239,

15 web codes: aue-0775, aue-0802, aua-0802, aua- 1003, aue-1003 PO 2. Identify the hierarchy of quadrilaterals SE/TE: 182, , , 334, 342, 358, TE: 310, 325, 326, 543, 545 PO 3. Make a net to represent a 3-dimensional object SE/TE: 12, 72, 609, 653 TE: 11, 13, 612, 613 web codes: auj-1051 PO 4. Make a 3-dimensional model from a net SE/TE: 12, 72, 609, 653 TE: 11, 13, 612, 613 web codes: auj-1051 PO 5. Draw 2-dimensional and 3-dimensional figures with appropriate labels SE/TE: 12, 16, 43, 183, 220, 227, 235, 356, 368, 407, 540, 541, 600, 605, 608, 609, , , , 654, 740 TE: 13, 184, 370, 543, 601, 620, 627 web codes: auj-0751, aue-2121, aue

16 PO 6. Solve problems related to complementary, supplementary, or congruent angle concepts SE/TE: 37, 38, 39, 45, 72, , 229 TE: 40, 42, 113, 114, 115 web codes: aue-0775 PO 7. Solve problems by applying the relationship between circles, angles, and intercepted arcs SE/TE: 273, 298, 546, 566, , 589, 591, , , , 708, 765 TE: 547, 570, 572, 682, 683, 684 web codes: auj-1051 PO 8. Solve problems by applying the relationship between radii, diameters, chords, tangents, or secants SE/TE: 546, 566, 589, 638, 662, , , , 683, , 689, , TE: 547, 567 web codes: auj-1051, aue-1203 PO 9. Solve problems using the triangle inequality property SE/TE: , 299 TE: 294 PO 10. Solve problems using special case right triangles SE/TE: 148, 229, , , 419, , 427, 429, 541, 764 TE: 231, 238, 239, 394, 395,

17 web codes: aue-0775, aue-0802, aua-0802 PO 11. Determine when triangles are congruent by applying SSS, ASA, AAS, or SAS. SE/TE: 205, , , 215, 561 TE: 208, 210, 216, 218, 560, 562 web codes: aue-0775 PO 12. Determine when triangles are similar by applying SAS, SSS, or AA similarity postulates SE/TE: , 250, , 373, 382, , 385, , 397, 408, 433, 561 TE: 208, 210, 387, 395, 560, 562 web codes: aue-0775, aue-0653 PO 13. Construct a triangle congruent to a given triangle SE/TE: 199, 200, 204, 207, 209, 210, 220, , 242, 243, 250 TE: 201, 202, 208, 223, 244, 245 web codes: aue-0775, aue-0420 PO 14. Solve contextual situations using angle and side length relationships. SE/TE: 205, , , 215, 250, , 373, 382, , 385, , 397, 408, 433, 561 TE: 208, 210, 216, 218, 387, 395, 560,

18 web codes: aue-0775, aue-0653 Concept 2: Transformation of Shapes Apply spatial reasoning to create transformations and use symmetry to analyze mathematical situations. PO 1. Sketch the planar figure that is the result of two or more transformations SE/TE: , 489, , , 523, TE: 473, 475, 518 web codes: auj-0951 PO 2. Identify the properties of the planar figure that is the result of two or more transformations SE/TE: , 489, , , 523, TE: 473, 475, 518 web codes: auj-0951 PO 3. Determine the new coordinates of a point when a single transformation is performed on a planar geometric figure SE/TE: , , , , 506, 515, 516, 517, 523, PO 4. Determine whether a given pair of figures on a coordinate plane represents a translation, reflection, rotation, or dilation TE: 473, 475, 500, 501, 502, 518 web codes: auj-0951 SE/TE: , , , , 506, 515, 516, 517, 523, TE: 473, 475, 500, 501, 502,

19 PO 5. Classify transformations based on whether they produce congruent or similar figures web codes: auj-0951 SE/TE: , , , , 506, 515, 516, 517, 523, TE: 473, 475, 500, 501, 502, 518 web codes: auj-0951 PO 6. Determine the effects of a single transformation on linear or area measurements of a planar geometric figure. SE/TE: , , , , 506, 515, 516, 517, 523, TE: 473, 475, 500, 501, 502, 518 web codes: auj-0951 Concept 3: Coordinate Geometry Specify and describe spatial relationships using coordinate geometry and other representational systems. PO 1. Graph a quadratic equation with lead coefficient equal to one SE/TE: 372 PO 2. Graph a linear equation in two variables SE/TE: , 168, , 175, 176, 234, 760, 765 TE: 169, 177, 179 web code: aue-0775 PO 3. Graph a linear inequality in two variables SE/TE: 288, , , 299 TE:

20 PO 4. Determine the solution to a system of equations in two variables from a given graph SE/TE: , 168, , 175, 176, 234, 760, 765 TE: 169, 177, 179 web codes: aue-0775 PO 5. Determine the midpoint between two points in a coordinate system SE/TE: 32, 33, 54-55, 70, 72, 73, 260, 765 TE: 35, 56 PO 6. Determine changes in the graph of a linear function when constants and coefficients in its equation are varied SE/TE: , 168, , 175, 176, 234, 248, 760, 765 TE: 169, 177, 179, 261, 262 PO 7. Determine the distance between two points in the coordinate system. SE/TE: 52-54, 266, 297 TE: 56, 267 web codes: auj

21 Concept 4: Measurement - Units of Measure - Geometric Objects Understand and apply appropriate units of measure, measurement techniques, and formulas to determine measurements. PO 1. Calculate the area of geometric shapes composed of two or more geometric figures SE/TE: 62, 63, 64, 73, , 559, , 589, 764, 765 TE: 65, 67, 537, 538, 578, 579 web codes: aue-0775, auj-1051 PO 2. Calculate the volumes of 3-dimensional geometric figures SE/TE: 608, 609, , , 619, , 654, 655, 765 TE: 612, 613, 620, 641, 643 web codes: aub-2031, aue-2101 PO 3. Calculate the surface areas of 3-dimensional geometric figures SE/TE: 608, 609, , , 619, , 654, 655, 765 TE: 612, 613, 620, 641, 643 web codes: aub-2031, aue-2101 PO 4. Compare perimeter, area, or volume of figures when dimensions are changed SE/TE: 69, 368, 407, PO 5. Find the length of a circular arc SE/TE: 569, 591, 765 TE: 570 TE: 370, 500, 501, 502 web codes: auj

22 PO 6. Find the area of a sector of a circle SE/TE: 62, 64, 73, , 765 TE: 65, 578, 579 PO 7. Solve for missing measures in a pyramid (i.e., slant height, height) SE/TE: 617, 618, , 654 TE: 619, 620, 634 PO 8. Find the sum of the interior and exterior angles of a polygon SE/TE: , 191 TE: 161 web codes: aue-0775 PO 9. Solve scale factor problems using ratios and proportions SE/TE: , 373, , 407, , 555, , 655 TE: 370, 401, 703, 500, 501, 502 web codes: auj-0751 PO 10. Solve applied problems using similar triangles. SE/TE: , 373, , , , 397, 408, 433 TE: 387, 394,

23 web codes: aue-0653 Strand 5: Structure and Logic Every student should understand and use all concepts and skills from the previous grade levels. The standards are designed so that new learning builds on preceding skills and are needed to learn new skills. Communication, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of mathematical strands. Concept 1: Algorithms and Algorithmic Thinking Use reasoning to solve mathematical problems in contextual situations. PO 1. Determine whether a given procedure for SE/TE: 754 simplifying an expression is valid PO 2. Determine whether a given procedure for solving an equation is valid PO 3. Determine whether a given procedure for solving a linear inequality is valid SE/TE: 754 SE/TE: 30, , 758 PO 4. Select an algorithm that explains a particular mathematical process PO 5. Determine the purpose of a simple mathematical algorithm web codes: Algebra 2. Algebra 2. PO 6. Determine whether given simple mathematical algorithms are equivalent. Algebra 2. Concept 2: Logic, Reasoning, Arguments, and Mathematical Proof Evaluate situations, select problem-solving strategies, draw logical conclusions, develop and describe solutions and recognize their applications. PO 1. Draw a simple valid conclusion from a given if then statement and a minor premise SE/TE: 4-6, 15, 49, 71, 94-96, , 118, , 159, 218, 233, 245, 270, , 298, 650, 744 TE: 97, 99, 106, 107, 284,

24 web codes: aue-0102, aua-0102, aue-0107, aua- 0107, aue-0407, aua-0407, aue-1107, aua-1107, aue-0253, aue-0775, aua-0405 PO 2. List related if then statements in logical order SE/TE: 4-6, 15, 49, 71, 94-96, , 118, , 159, 218, 233, 245, 270, , 298, 650, 744 TE: 97, 99, 106, 107, 284, 285 web codes: aue-0102, aua-0102, aue-0107, aua- 0107, aue-0407, aua-0407, aue-1107, aua-1107, aue-0253, aue-0775, aua-0405 PO 3. Write an appropriate conjecture given a certain set of circumstances SE/TE: 5-6, 27, 49, 69, 185, 204, 220, 227, , 269, 272, 320, 397, 424, 432, 438, 442, 477, 519, 645, 667, 669 TE: 184, 433, 518 web codes: aua-0104, aue-0104, aue-0107, aua- 0107, aue-0308, aua-0308, aue-0804, aua-0804, aue-0907, aua-0907, aue-1201, aua-1201 PO 4. Analyze assertions related to a contextual situation by using principles of logic SE/TE: 4-6, 15, 49, 71, 94-96, , 118, , 159, 218, 233, 245, 270, , 298, 650, 744 TE: 97, 99, 106, 107, 284,

25 web codes: aue-0102, aua-0102, aue-0107, aua- 0107, aue-0407, aua-0407, aue-1107, aua-1107, aue-0253, aue-0775, aua-0405 PO 5. Identify a valid conjecture using inductive reasoning SE/TE: 5-6, 27, 49, 69, 185, 204, 220, 227, , 269, 272, 320, 397, 424, 432, 438, 442, 477, 519, 645, 667, 669 TE: 184, 433, 518 web codes: aua-0104, aue-0104, aue-0107, aua- 0107, aue-0308, aua-0308, aue-0804, aua-0804, aue-0907, aua-0907, aue-1201, aua-1201 PO 6. Distinguish valid arguments from invalid arguments SE/TE: 4-6, 15, 49, 71, 94-96, , 118, , 159, 218, 233, 245, 270, , 298, 650, 744 TE: 97, 99, 106, 107, 284, 285 web codes: aue-0102, aua-0102, aue-0107, aua- 0107, aue-0407, aua-0407, aue-1107, aua-1107, aue-0253, aue-0775, aua-0405 PO 7. Create inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship SE/TE: 4-6, 15, 49, 71, 94-96, , 118, , 159, 218, 233, 245, 270, , 298, 650, 744 TE: 97, 99, 106, 107, 284,

26 web codes: aue-0102, aua-0102, aue-0107, aua- 0107, aue-0407, aua-0407, aue-1107, aua-1107, aue-0253, aue-0775, aua-0405 PO 8. Critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship SE/TE: 4-6, 15, 49, 71, 94-96, , 118, , 159, 218, 233, 245, 270, , 298, 650, 744 TE: 97, 99, 106, 107, 284, 285 web codes: aue-0102, aua-0102, aue-0107, aua- 0107, aue-0407, aua-0407, aue-1107, aua-1107, aue-0253, aue-0775, aua-0405 PO 9. Identify a counterexample for a given conjecture SE/TE: 5-6, 27, 49, 69, 185, 204, 220, 227, , 269, 272, 320, 397, 424, 432, 438, 442, 477, 519, 645, 667, 669 TE: 184, 433, 518 web codes: aua-0104, aue-0104, aue-0107, aua- 0107, aue-0308, aua-0308, aue-0804, aua-0804, aue-0907, aua-0907, aue-1201, aua-1201 PO 10. Construct a counterexample to show that a given conjecture is false SE/TE: 5-6, 27, 49, 69, 185, 204, 220, 227, , 269, 272, 320, 397, 424, 432, 438, 442, 477, 519, 645, 667, 669 TE: 184, 433,

27 web codes: aua-0104, aue-0104, aue-0107, aua- 0107, aue-0308, aua-0308, aue-0804, aua-0804, aue-0907, aua-0907, aue-1201, aua-1201 PO 11. State the inverse, converse, or contrapositive of a given statement. SE/TE: 81-84, 117, 134, , 228, 230, 251, 265, 266, , 298, 299, , 402, 419, 423, 434, 440, 461 TE: 86, 139, 229, 231, 267, 283, 331, 332, 420, 435, 441 web codes: aug-0251, aue-0802, aue-0705, aua- 0705, auj-0851 PO 12. Determine if the inverse, converse, or SE/TE: 81-84, 117, 134, , 228, 230, contrapositive of a given statement is true or false. 251, 265, 266, , 298, 299, , 402, 419, 423, 434, 440, 461 TE: 86, 139, 229, 231, 267, 283, 331, 332, 420, 435, 441 web codes: aug-0251, aue-0802, aue-0705, aua- 0705, auj-0851 PO 13. Construct a simple formal or informal deductive proof. SE/TE: 147, 200, 207, 209, 210, 214, 215, 235, 260, , 289, 290, 291, 346, 383, 398, 400, 663, 683, 688, 689 TE: 201, 208, 216, 262, 284, 285, 292, 384, 285, 399, 401, 664, 690, 691 web codes: aue-0775, aue-0402, aue

28 PO 14. Verify characteristics of a given geometric figure using coordinate formulas such as distance, mid-point, and slope to confirm parallelism, perpendicularity, and congruency. SE/TE: 37, 45, 53, 55, 60, 70, 73, 105, 119, 165, , 191, 206, 260, 306, , 357, 421, 695, 696, 765 TE: 40, 47, 54, 106, 107, 179, 207, 262, 307, 317, 422, 698, 699 web codes: aue-0775, auj-0651, aue