PROOF, PARALLEL AND PERPENDICULAR LINES Planning the Unit Unit 1 Overview 1 Getting Ready 2


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1 vx_sb_geo_te_toc.indd Page 5 15/04/14 1:56 PM usergw728 To the Teacher Instructional Units UNIT 1 PROOF, PARALLEL AND PERPENDICULAR LINES 1a Unit 1 Overview 1 Getting Ready 2 Activity 1 Geometric Figures What's My Name? 3 Lesson 11 Basic Geometric Figures 3 Lesson 12 More Geometric Figures 7 Activity 1 Practice 11 Activity 2 Logical Reasoning Riddle Me This 13 Lesson 21 Inductive Reasoning 13 Lesson 22 Deductive Reasoning 18 Activity 2 Practice 23 Activity 3 The Axiomatic System of Geometry Back to the Beginning 25 Lesson 31 Geometric Definitions and TwoColumn Proofs 25 Lesson 32 Conditional Statements 29 Lesson 33 Converse, Inverse, and Contrapositive 32 Activity 3 Practice 35 Embedded Assessment 1 Geometric Figures and Basic Reasoning The Art and Math of Folding Paper 37 Activity 4 Segment and Angle Measurement It All Adds Up 39 Lesson 41 Segments and Midpoints 39 Lesson 42 Angles and Angle Bisectors 45 Activity 4 Practice 49 Activity 5 The Distance and Midpoint Formulas We Descartes 51 Lesson 51 Distance on the Coordinate Plane 51 Lesson 52 Midpoint on the Coordinate Plane 56 Activity 5 Practice 59 Embedded Assessment 2 Distance, Midpoint, and Angle Measurement A Walk in the Park 61 Activity 6 Proofs about Line Segments and Angles Now I m Convinced 63 Lesson 61 Justifying Statements 63 Lesson 62 TwoColumn Geometric Proofs 66 Activity 6 Practice 71 Activity 7 Parallel and Perpendicular Lines Patios by Madeline 73 Lesson 71 Parallel Lines and Angle Relationships 73 Lesson 72 Proving Lines are Parallel 79 Lesson 73 Perpendicular Lines 84 Activity 7 Practice 87 xi v
2 vx_sb_geo_te_toc.indd Page 6 15/04/14 1:56 PM usergw728 continued Activity 8 Equations of Parallel and Perpendicular Lines Skateboard Geometry 89 Lesson 81 Slopes of Parallel and Perpendicular Lines 89 Lesson 82 Writing Equations 92 Activity 8 Practice 97 Embedded Assessment 3 Angles, Parallel Lines, and Perpendicular Lines Graph of Steel 99 UNIT 2 TRANSFORMATIONS, TRIANGLES, AND QUADRILATERALS 101a Unit 2 Overview 101 Getting Ready 102 Activity 9 Translations, Reflections, and Rotations The Marching Cougars 103 Lesson 91 Transformations 103 Lesson 92 Translations 108 Lesson 93 Reflection 112 Lesson 94 Rotations 120 Activity 9 Practice 127 Activity 10 Compositions and Congruence More Rigid Motions 129 Lesson 101 Compositions of Transformations 129 Lesson 102 Congruence 134 Activity 10 Practice 139 Embedded Assessment 1 Transformations Designing the Plaza 141 Activity 11 Congruence Transformations and Triangle Congruence Truss Your Judgment 143 Lesson 111 Congruent Triangles 143 Lesson 112 Congruence Criteria 147 Lesson 113 Proving and Applying the Congruence Criteria 154 Lesson 114 Extending the Congruence Criteria 160 Activity 11 Practice 165 Activity 12 Flowchart Proofs Go with the Flow 167 Lesson 121 Flowchart Proofs 167 Lesson 122 Three Types of Proofs 175 Activity 12 Practice 177 Embedded Assessment 2 Congruence, Triangles, and Proof Building a Fitness Center 179 Activity 13 Properties of Triangles Best Two Out of Three 181 Lesson 131 Angle Relationships in Triangles 181 Lesson 132 Isosceles Triangles 186 Activity 13 Practice 189 vi SpringBoard Mathematics Geometry
3 vx_sb_geo_te_toc.indd Page 7 15/04/14 1:56 PM usergw728 Activity 14 Concurrent Segments in Triangles What s the Point? 191 Lesson 141 Altitudes of a Triangle 191 Lesson 142 Medians of a Triangle 195 Lesson 143 Perpendicular Bisectors and Angle Bisectors of a Triangle 198 Activity 14 Practice 201 Embedded Assessment 3 Properties of Triangles Where Does the Fountain Go? 203 Activity 15 Quadrilaterals and Their Properties A 4gon Hypothesis 205 Lesson 151 Kites and Triangle Midsegments 205 Lesson 152 Trapezoids 209 Lesson 153 Parallelograms 213 Lesson 154 Rectangles, Rhombuses, and Squares 216 Activity 15 Practice 221 Activity 16 More About Quadrilaterals A 4gon Conclusion 223 Lesson 161 Proving a Quadrilateral is a Parallelogram 223 Lesson 162 Proving a Quadrilateral is a Rectangle 227 Lesson 163 Proving a Quadrilateral is a Rhombus 230 Lesson 164 Proving a Quadrilateral is a Square 233 Activity 16 Practice 235 Embedded Assessment 4 Quadrilaterals Lucy Latimer s Logo 237 UNIT 3 SIMILARITY AND TRIGONOMETRY 239a Unit 3 Overview 239 Getting Ready 240 Activity 17 Dilations and Similarity Transformations Scaling Up/ Scaling Down 241 Lesson 171 Dilations 241 Lesson 172 Similarity Transformations 248 Lesson 173 Properties of Similar Figures 252 Activity 17 Practice 255 Activity 18 Similar Triangles Measuring Up 257 Lesson 181 Similarity Criteria 257 Lesson 182 Using Similarity Criteria 262 Lesson 183 Triangle Proportionality Theorem 265 Activity 18 Practice 271 Embedded Assessment 1 Similarity in Polygons Monitoring Progress 273 Activity 19 Geometric Mean Do You Mean It? 275 Lesson 191 The Right Triangle Altitude Theorem 275 Lesson 192 The Geometric Mean 278 Activity 19 Practice 281 Activity 20 The Pythagorean Theorem and Its Converse Is That Right? 283 Lesson 201 Pythagorean Theorem 283 Lesson 202 Converse of the Pythagorean Theorem 286 Activity 20 Practice 289 vii
4 vx_sb_geo_te_toc.indd Page 8 15/04/14 1:56 PM usergw728 continued Activity 21 Special Right Triangles The Community Quilting Project 291 Lesson Triangles 291 Lesson Triangles 295 Activity 21 Practice 299 Embedded Assessment 2 Right Triangles Powered by the Wind 301 Activity 22 Basic Trigonometric Relationships The Sine of Things to Come 303 Lesson 221 Similar Right Triangles 303 Lesson 222 Trigonometric Ratios 308 Lesson 223 Using Trigonometric Ratios 312 Lesson 224 Solving Right Triangles 315 Activity 22 Practice 317 Activity 23 The Laws of Sines and of Cosines There Ought to Be a Law 319 Lesson 231 The Law of Sines 319 Lesson 232 The Ambiguous Case 322 Lesson 233 The Law of Cosines 324 Lesson 234 Solving Triangles 327 Activity 23 Practice 329 Embedded Assessment 3 Trigonometry Zipping Along 331 UNIT 4 CIRCLES, COORDINATES, AND CONSTRUCTIONS 333a Unit 4 Overview 333 Getting Ready 334 Activity 24 Tangents and Chords Off On a Tangent 335 Lesson 241 Circle Basics 335 Lesson 242 Theorems About Chords 339 Lesson 243 Tangent Segments 345 Activity 24 Practice 347 Activity 25 Arcs and Angles Coming Full Circle 349 Lesson 251 Arcs and Central Angles 349 Lesson 252 Inscribed Angles 353 Lesson 253 Angles Formed by Chords 358 Lesson 254 Angles Formed by Tangents and Secants 363 Activity 25 Practice 369 Embedded Assessment 1 Circles Vertigo Round 371 Activity 26 Coordinate Proofs Prove It! 373 Lesson 261 Proving the Midpoint Formula 373 Lesson 262 Proofs about Slope 377 Lesson 263 Proving Concurrency of Medians 382 Lesson 264 Points Along a Line Segment 387 Activity 26 Practice 390 viii SpringBoard Mathematics Geometry
5 vx_sb_geo_te_toc.indd Page 9 15/04/14 1:56 PM usergw728 Activity 27 Equation of a Circle Round and Round 391 Lesson 271 Circles on the Coordinate Plane 391 Lesson 272 Completing the Square to Find the Center and Radius 396 Activity 27 Practice 399 Activity 28 Equations of Parabolas Throwing a Curve 401 Lesson 281 Parabolas on the Coordinate Plane 401 Lesson 282 Parabolas with Vertex (h, k) 405 Activity 28 Practice 409 Activity 29 Constructions Constructive Thinking 411 Lesson 291 Constructions with Segments and Angles 411 Lesson 292 Constructions with Parallel and Perpendicular Lines 418 Lesson 293 Constructions with Circles 422 Activity 29 Practice 427 Embedded Assessment 2 Coordinates and Constructions Location Matters 429 UNIT 5 EXTENDING TWO DIMENSIONS TO THREE DIMENSIONS 431a Unit 5 Overview 431 Getting Ready 432 Activity 30 Deriving Area Formulas Shape Up 433 Lesson 301 Areas of Rectangles and Parallelograms 433 Lesson 302 Areas of Triangles 437 Lesson 303 Areas of Rhombuses and Trapezoids 441 Activity 30 Practice 445 Activity 31 Regular Polygons Plenty of Polygons 447 Lesson 311 Sum of the Measures of the Interior Angles of a Polygon 447 Lesson 312 Regular Polygons and Exterior Angles 453 Lesson 313 Area and Perimeter of Regular Polygons 457 Activity 31 Practice 461 Activity 32 Length and Area of Circles Pi in the Sky 463 Lesson 321 Circumference and Area of a Circle 463 Lesson 322 Sectors and Arcs 467 Lesson 323 Circles and Similarity 470 Activity 32 Practice 475 Embedded Assessment 1 Area and Perimeter Play Planning 477 Activity 33 ThreeDimensional Figures What s Your View? 479 Lesson 331 Prisms and Pyramids 479 Lesson 332 Cylinders and Cones 486 Lesson 333 Spheres and Solids of Rotation 489 Activity 33 Practice 493 Activity 34 Prisms and Cylinders Exterior Experiences 495 Lesson 341 Surface Area of Prisms and Cylinders 495 Lesson 342 Volume of Prisms and Cylinders 500 Activity 34 Practice 505 ix
6 vx_sb_geo_te_toc.indd Page 10 15/04/14 1:56 PM usergw728 continued Activity 35 Pyramids and Cones Perfect Packaging 507 Lesson 351 Surface Area of Pyramids and Cones 507 Lesson 352 Volume of Pyramids and Cones 513 Lesson 353 Density 518 Activity 35 Practice 521 Embedded Assessment 2 Surface Area and Volume ActionPacked Measurements 523 Activity 36 Spheres Isn t that Spatial? 525 Lesson 361 Surface Area of Spheres 525 Lesson 362 Volume of Spheres 529 Lesson 363 Spherical Geometry 532 Activity 36 Practice 537 Activity 37 Changing Dimensions Model Behavior 539 Lesson 371 Cubes and Spheres 539 Lesson 372 Pyramids and Cylinders 542 Activity 37 Practice 547 Embedded Assessment 3 Changing Dimensions of Spheres Spherical Storage 549 UNIT 6 PROBABILITY 551a Unit 6 Overview 551 Getting Ready 552 Activity 38 Sample Spaces SpringBoard Superstar and More 553 Lesson 381 Probability of a Single Event 553 Lesson 382 Events Involving And and Or 559 Activi ty 38 Practice 565 Activity 39 Venn Diagrams and Probability Notation Annabel HS 567 Lesson 391 Using a Venn Diagram to Represent a Sample Space 567 Lesson 392 Using Venn Diagrams to Represent And, Or, and Not 573 Activity 39 Practice 579 Activity 40 Addition Rule and Mutually Exclusive Events Hector Street 581 Lesson 401 Applying the Addition Rule 581 Lesson 402 Adapting the Addition Rule for Mutually Exclusive Events 587 Activity 40 Practice 591 Embedded Assessment 1 Probability and the Addition Rule Diane s Books 593 Activity 41 Dependent Events Coco Wildlife Conservation Trust 595 Lesson 411 Understanding Conditional Probability 595 Lesson 412 The Conditional Probability Formula 601 Lesson 413 Tree Diagrams 604 Activity 41 Practice 611 x SpringBoard Mathematics Geometry
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