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KCP - Discovering Geometry c2008
Mathematics - Grade 10

 
  CHAPTER KCP.0. Chapter 0: Geometric Art
    SECTION KCP.0.1. Ch 0 Section 1: Geometry in Nature and in Art (pp. 2 - 4)
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    SECTION KCP.0.2. Ch 0 Section 2: Line Designs (pp. 7 - 8)
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    SECTION KCP.0.3. Ch 0 Section 3: Circle Designs (pp. 10 - 11)
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    SECTION KCP.0.4. Ch 0 Section 4: Op Art (pp. 13 - 14)
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    SECTION KCP.0.5. Ch 0 Section 5: Knot Designs (pp. 16 - 17)
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    SECTION KCP.0.6. Ch 0 Section 6: Islamic Tile Designs (pp. 20 - 22)
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  CHAPTER KCP.1. Chapter 1: Introducing Geometry
    SECTION KCP.1.1. Ch 1 Section 1: Building Blocks of Geometry (pp. 28 - 32)
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    SECTION KCP.1.AS. Ch 1 Using Your Algebra Skills 1: Midpoint (pp. 36 - 37)
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    SECTION KCP.1.2. Ch 1 Section 2: Poolroom Math (pp. 38 - 42)
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    SECTION KCP.1.3. Ch 1 Section 3: What's a Widget? (pp. 47 - 51)
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    SECTION KCP.1.4. Ch 1 Section 4: Polygons (pp. 54 - 56)
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    SECTION KCP.1.5. Ch 1 Section 5: Triangles (pp. 59 - 61)
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    SECTION KCP.1.6. Ch 1 Section 6: Special Quadrilaterals (pp. 64 - 65)
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    SECTION KCP.1.7. Ch 1 Section 7: Circles (pp. 69 - 71)
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    SECTION KCP.1.8. Ch 1 Section 8: Space Geometry (pp. 75 - 77)
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    SECTION KCP.1.9. Ch 1 Section 9: A Picture Is Worth a Thousand Words (pp. 81 - 83)
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    SECTION KCP.1.Exp. Ch 1 Exploration: Geometric Probability I (pp. 88 - 89)
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  CHAPTER KCP.2. Chapter 2: Reasoning in Geometry
    SECTION KCP.2.1. Ch 2 Section 1: Inductive Reasoning (pp. 96 - 98)
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    SECTION KCP.2.2. Ch 2 Section 2: Finding the nth Term (pp. 102 - 104)
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    SECTION KCP.2.3. Ch 2 Section 3: Mathematical Modeling (pp. 108 - 111)
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    SECTION KCP.2.4. Ch 2 Section 4: Deductive Reasoning (pp. 114 - 116)
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    SECTION KCP.2.Exp. Ch 2 Exploration: The Seven Bridges of Konigsberg (pp. 120 - 121)
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    SECTION KCP.2.5. Ch 2 Section 5: Angle Relationships (pp. 122 - 124)
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    SECTION KCP.2.6. Ch 2 Section 6: Special Angles on Parallel Lines (pp. 128 - 131)
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    SECTION KCP.2.AS. Ch 2 Using Your Algebra Skills 2: Slope (pp. 135 - 136)
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  CHAPTER KCP.3. Chapter 3: Using Tools of Geometry
    SECTION KCP.3.1. Ch 3 Section 1: Duplicating Segments and Angles (pp. 144 - 146)
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    SECTION KCP.3.2. Ch 3 Section 2: Constructing Perpendicular Bisectors (pp. 149 - 151)
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    SECTION KCP.3.3. Ch 3 Section 3: Constructing Perpendiculars to a Line (pp. 154 - 156)
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    SECTION KCP.3.4. Ch 3 Section 4: Constructing Angle Bisectors (pp. 159 - 160)
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    SECTION KCP.3.5. Ch 3 Section 5: Constructing Parallel Lines (pp. 163 - 164)
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    SECTION KCP.3.AS. Ch 3 Using Your Algebra Skills 3: Slope of Parallel and Perpendicular Lines (pp. 167 - 168)
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    SECTION KCP.3.6. Ch 3 Section 6: Construction Problems (pp. 170 - 171)
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    SECTION KCP.3.Exp1. Ch 3 Exploration: Perspective Drawing (pp. 174 - 177)
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    SECTION KCP.3.7. Ch 3 Section 7: Constructing Points of Concurrency (pp. 178 - 181)
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    SECTION KCP.3.8. Ch 3 Section 8: The Centroid (pp. 185 - 187)
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    SECTION KCP.3.Exp2. Ch 3 Exploration: The Euler Line (pp. 191 - 193)
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  CHAPTER KCP.4. Chapter 4: Discovering and Proving Triangle Properties
    SECTION KCP.4.1. Ch 4 Section 1: Triangle Sum Conjecture (pp. 200 - 202)
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    SECTION KCP.4.2. Ch 4 Section 2: Properties of Isosceles Triangles (pp. 206 - 208)
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    SECTION KCP.4.AS. Ch 4 Using Your Algebra Skills 4: Solving Equations (pp. 212 - 213)
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    SECTION KCP.4.3. Ch 4 Section 3: Triangle Inequalities (pp. 215 - 218)
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    SECTION KCP.4.4. Ch 4 Section 4: Are There Congruence Shortcuts? (pp. 221 - 223)
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    SECTION KCP.4.5. Ch 4 Section 5: Are There Other Congruence Shortcuts? (pp. 227 - 229)
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    SECTION KCP.4.6. Ch 4 Section 6: Corresponding Parts of Congruent Triangles (pp. 232 - 233)
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    SECTION KCP.4.7. Ch 4 Section 7: Flowchart Thinking (pp. 237 - 239)
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    SECTION KCP.4.8. Ch 4 Section 8: Proving Special Triangle Conjectures (pp. 243 - 245)
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    SECTION KCP.4.Exp. Ch 4 Exploration: Napoleon's Theorem (pp. 249 - 250)
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  CHAPTER KCP.5. Chapter 5: Discovering and Proving Polygon Properties
    SECTION KCP.5.1. Ch 5 Section 1: Polygon Sum Conjecture (pp. 258 - 259)
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    SECTION KCP.5.2. Ch 5 Section 2: Exterior Angles of a Polygon (pp. 262 - 263)
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    SECTION KCP.5.Exp. Ch 5 Exploration; Star Polygons (pp. 266 - 267)
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    SECTION KCP.5.3. Ch 5 Section 3: Kite and Trapezoid Properties (pp. 268 - 271)
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    SECTION KCP.5.4. Ch 5 Section 4: Properties of Midsegments (pp. 275 - 277)
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    SECTION KCP.5.5. Ch 5 Section 5: Properties of Parallelograms (pp. 281 - 283)
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    SECTION KCP.5.AS. Ch 5 Using Your Algebra Skills 5: Writing Linear Equations (pp. 287 - 289)
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    SECTION KCP.5.6. Ch 5 Section 6: Properties of Special Parallelograms (pp. 291 - 294)
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    SECTION KCP.5.7. Ch 5 Section 7: Proving Quadrilateral Properties (pp. 298 - 300)
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  CHAPTER KCP.6. Chapter 6: Discovering and Proving Circle Properties
    SECTION KCP.6.1. Ch 6 Section 1: Tangent Properties (pp. 310 - 313)
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    SECTION KCP.6.2. Ch 6 Section 2: Chord Properties (pp. 317 - 320)
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    SECTION KCP.6.3. Ch 6 Section 3: Arcs and Angles (pp. 324 - 327)
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    SECTION KCP.6.4. Ch 6 Section 4: Proving Circle Conjectures (pp. 330 - 332)
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    SECTION KCP.6.5. Ch 6 Section 5: The Circumference/Diameter Ratio (pp. 335 - 337)
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    SECTION KCP.6.6. Ch 6 Section 6: Around the World (pp. 341)
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    SECTION KCP.6.AS. Ch 6 Using Your Algebra Skills 6: Solving Systems of Linear Equations (pp. 345 - 347)
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    SECTION KCP.6.7. Ch 6 Section 7: Arc Length (pp. 349 - 351)
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    SECTION KCP.6.Exp. Ch 6 Exploration: Intersecting Lines Through a Circle (pp. 355 - 359)
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  CHAPTER KCP.7. Chapter 7: Transformations and Tessellations
    SECTION KCP.7.1. Ch 7 Section 1: Transformations and Symmetry (pp. 368 - 372)
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    SECTION KCP.7.2. Ch 7 Section 2: Properties of Isometries (pp. 376 - 380)
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    SECTION KCP.7.3. Ch 7 Section 3: Compositions of Transformations (pp. 383 - 386)
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    SECTION KCP.7.4. Ch 7 Section 4: Tessellations with Regular Polygons (pp. 389 - 391)
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    SECTION KCP.7.5. Ch 7 Section 5: Tessellations with Nonregular Polygons (pp. 394 - 395)
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    SECTION KCP.7.6. Ch 7 Section 6: Tessellations Using Only Translations (pp. 399 - 400)
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    SECTION KCP.7.7. Ch 7 Section 7: Tessellation That Use Rotations (pp. 403 - 405)
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    SECTION KCP.7.Exp. Ch 7 Exploration: Tessellating with the Conway Criterion (pp. 408 - 409)
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    SECTION KCP.7.8. Ch 7 Section 8: Tessellations That Use Glide Reflections (pp. 410 - 411)
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    SECTION KCP.7.AS. Ch 7 Using Your Algebra Skills 7: Finding Points of Concurrency (pp. 413 - 415)
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  CHAPTER KCP.8. Chapter 8: Area
    SECTION KCP.8.1. Ch 8 Section 1: Areas of Rectangles and Parallelograms (pp. 422 - 425)
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    SECTION KCP.8.2. Ch 8 Section 2: Areas of Triangles, Trapezoids, and Kites (pp. 429 - 430)
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    SECTION KCP.8.3. Ch 8 Section 3: Area Problems (pp. 434 - 435)
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    SECTION KCP.8.AS. Ch 8 Using Your Algebra Skills 8: Products, Factors, and Quadratic Equations (pp. 438 - 440)
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    SECTION KCP.8.4. Ch 8 Section 4: Areas of Regular Polygons (pp. 442 - 443)
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    SECTION KCP.8.Exp1. Ch 8 Exploration: Pick's Formula for Area (pp. 446 - 448)
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    SECTION KCP.8.5. Ch 8 Section 5: Areas of Circles (pp. 449 - 450)
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    SECTION KCP.8.6. Ch 8 Section 6: Any Way You Slice It (pp. 453 - 454)
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    SECTION KCP.8.Exp2. Ch 8 Exploration: Geometric Probability II (pp. 458 - 460)
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    SECTION KCP.8.7. Ch 8 Section 7: Surface Area (pp. 461 - 465)
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    SECTION KCP.8.Exp3. Ch 8 Exploration: Alternative Area Formulas (pp. 469 - 470)
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  CHAPTER KCP.9. Chapter 9: The Pythagorean Theorem
    SECTION KCP.9.1. Ch 9 Section 1: The Theorem of Pythagoras (pp. 478 - 480)
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    SECTION KCP.9.2. Ch 9 Section 2: The Converse of the Pythagorean Theorem (pp. 484 - 486)
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    SECTION KCP.9.AS. Ch 9 Using Your Algebra Skills 9: Radical Expressions (pp. 489 - 490)
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    SECTION KCP.9.3. Ch 9 Section 3: Two Special Right Triangles (pp. 491 - 493)
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    SECTION KCP.9.Exp1. Ch 9 Exploration: A Pythagorean Fractal (pp. 496 - 497)
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    SECTION KCP.9.4. Ch 9 Section 4: Story Problems (pp. 498)
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    SECTION KCP.9.5. Ch 9 Section 5: Distance in Coordinate Geometry (pp. 502 - 504)
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    SECTION KCP.9.Exp2. Ch 9 Exploration: Ladder Climb (pp. 507)
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    SECTION KCP.9.6. Ch 9 Section 6: Circles and the Pythagorean Theorem (pp. 508 - 509)
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  CHAPTER KCP.10. Chapter 10: Volume
    SECTION KCP.10.1. Ch 10 Section 1: The Geometry of Solids (pp. 520 - 524)
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    SECTION KCP.10.Exp1. Ch 10 Exploration: Euler's Formula for Polyhedrons (pp. 528 - 529)
    SECTION KCP.10.2. Ch 10 Section 2: Volume of Prisms and Cylinders (pp. 530 - 533)
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    SECTION KCP.10.3. Ch 10 Section 3: Volume of Pyramids and Cones (pp. 538 - 540)
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    SECTION KCP.10.Exp2. Ch 10 Exploration: The Five Platonic Solids (pp. 544 - 546)
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    SECTION KCP.10.4. Ch 10 Section 4: Volume Problems (pp. 547)
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    SECTION KCP.10.5. Ch 10 Section 5: Displacement and Density (pp. 551 - 552)
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    SECTION KCP.10.Exp3. Ch 10 Exploration: Orthographic Drawing (pp. 555 - 557)
    SECTION KCP.10.6. Ch 10 Section 6: Volume of a Sphere (pp. 558 - 559)
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    SECTION KCP.10.7. Ch 10 Section 7: Surface Area of a Sphere (pp. 562 - 563)
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    SECTION KCP.10.AS. Ch 10 Using Your Algebra Skills 10: Solving for Any Variable (pp. 567 - 567)
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    SECTION KCP.10.Exp. Ch 10 Exploration: Sherlock Holmes and Forms of Valid Reasoning (pp. 569 - 571)
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  CHAPTER KCP.11. Chapter 11: Similarity
    SECTION KCP.11.AS. Ch 11 Using Your Algebra Skills 11: Proportion and Reasoning (pp. 578 - 579)
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    SECTION KCP.11.1. Ch 11 Section 1: Similar Polygons (pp. 581 - 585)
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    SECTION KCP.11.2. Ch 11 Section 2: Similar Triangles (pp. 589 - 591)
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    SECTION KCP.11.Exp1. Ch 11 Exploration: Constructing a Dilation Design (pp. 595 - 597)
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    SECTION KCP.11.3. Ch 11 Section 3: Indirect Measurement with Similar Triangles (pp. 598 - 599)
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    SECTION KCP.11.4. Ch 11 Section 4: Corresponding Pars of Similar Triangles (pp. 603 - 605)
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    SECTION KCP.11.5. Ch 11 Section 5: Proportions with Area (pp. 608 - 610)
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    SECTION KCP.11.6. Ch 11 Section 6: Proportions with Volume (pp. 614 - 616)
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    SECTION KCP.11.Exp2. Ch 11 Exploration: Why Elephants Have Big Ears (pp. 620 - 622)
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    SECTION KCP.11.7. Ch 11 Section 7: Proportional Segments Between Parallel Lines (pp. 623 - 627)
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    SECTION KCP.11.Exp3. Ch 11 Exploration: Two More Forms of Valid Reasoning (pp. 631 - 633)
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  CHAPTER KCP.12. Chapter 12: Trigonometry
    SECTION KCP.12.1. Ch 12 Section 1: Trigonometric Ratios (pp. 640 - 644)
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    SECTION KCP.12.2. Ch 12 Section 2: Problem Solving with Right Triangles (pp. 647)
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    SECTION KCP.12.Exp1. Ch 12 Exploration: Indirect Measurement (pp. 652 - 653)
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    SECTION KCP.12.3. Ch 12 Section 3: The Law of Sines (pp. 654 - 657)
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    SECTION KCP.12.4. Ch 12 Section 4: The Law of Cosines (pp. 661 - 663)
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    SECTION KCP.12.5. Ch 12 Section 5: Problem Solving with Trigonometry (pp. 667)
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    SECTION KCP.12.Exp2. Ch 12 Exploration: Trigonometric Ratios and the Unit Circle (pp. 671 - 674)
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    SECTION KCP.12.AS. Ch 12 Using Your Algebra Skills 12: Transforming Functions (pp. 675 - 677)
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    SECTION KCP.12.Exp3. Ch 12 Exploration: Three Types of Proofs (pp. 679 - 682)
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  CHAPTER KCP.13. Chapter 13: Geometry as a Mathematical System
    SECTION KCP.13.1. Ch 13 Section 1: The Premises of Geometry (pp. 692 - 698)
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    SECTION KCP.13.2. Ch 13 Section 2: Planning a Geometry Proof (pp. 703 - 708)
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    SECTION KCP.13.3. Ch 13 Section 3: Triangle Proofs (pp. 710 - 712)
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    SECTION KCP.13.4. Ch 13 Section 4: Quadrilateral Proofs (pp. 716 - 717)
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    SECTION KCP.13.Exp1. Ch 13 Exploration: Proof as Challenge and Discovery (pp. 720 - 721)
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    SECTION KCP.13.5. Ch 13 Section 5: Indirect Proof (pp. 722 - 724)
    SECTION KCP.13.6. Ch 13 Section 6: Circle Proofs (pp. 727 - 728)
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    SECTION KCP.13.7. Ch 13 Section 7: Similarity Proofs (pp. 730 - 733)
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    SECTION KCP.13.AS. Ch 13 Using Your Algebra Skills 13: Coordinate Proof (pp. 736 - 739)
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    SECTION KCP.13.Exp2. Ch 13 Exploration: Non-Euclidean Geometries (pp. 742 - 744)