# SpringBoard Geometry SpringBoard Geometry

| ISBN: 9781457301520 / 1457301520

1,639

expert-verified solutions in this book

| ISBN: 9781457301520 / 1457301520

1,639

expert-verified solutions in this book

### Chapter 1

Geometric Figures-What's My Name?

 1.1 Basic Geometric Figures Learning Targets p.3 1.2 More Geometric Figures Learning Targets p.7 Activity Practice p.11

### Chapter 2

Logical Reasoning-Riddle Me This

 2.1 Inductive Reasoning Learning Targets p.13 2.2 Deductive Reasoning Learning Targets p.18 Activity Practice p.23

### Chapter 3

The Axiomatic System Of Geometry- Back To …

 3.1 Geometric Definitions and Two-Column Proofs Learning Targets p.25 3.2 Conditional Statements Learning Targets p.29 3.3 Converse, Inverse, and Contrapositive Learning Targets p.32 Activity Practice p.35

### Chapter 4

Segment And Angle Measurement-It All Adds Up

 4.1 Segments and Midpoints Learning Targets p.40 4.2 Angles and Angle Bisectors Learning Targets p.45 Activity Practice p.49

### Chapter 5

The Distance And Midpoint Formulas-We ❤ Descartes

 5.1 Distance on the Coordinate Plane Learning Targets p.51 5.2 Midpoint on the Coordinate Plane Learning Targets p.56 Activity Practice p.59

### Chapter 6

Proofs About Line Segments And Angles-Now I'M …

 6.1 Justifying Statements Learning Targets p.65 6.2 Two-Column Geometric Proofs Learning Targets p.69 Activity Practice p.71

### Chapter 7

Parallel And Perpendicular Lines-Patios By Madeline

 7.1 Parallel Lines and Angle Relationships Learning Targets p.74 7.2 Proving Lines are Parallel Learning Targets p.79 7.3 Perpendicular Lines Learning Targets p.84 Activity Practice p.87

### Chapter 8

Equations Of Parallel And Perpendicular Lines-Skateboard Geometry

 8.1 Slopes of Parallel and Perpendicular Lines Learning Targets p.89 8.2 Writing Equations Learning Targets p.92 Activity Practice p.97

### Chapter 9

Translations, Reflections, And Rotations-The Marching Cougars

 9.1 Transformations Learning Targets p.103 9.2 Translations Learning Targets p.108 9.3 Reflections Learning Targets p.112 9.4 Rotations Learning Targets p.120 Activity Practice p.127

### Chapter 10

Compositions And Congruence-More Rigid Motions

 10.1 Compositions of Transformations Learning Targets p.129 10.2 Congruence Learning Targets p.134 Activity Practice p.139

### Chapter 11

Congruence Transformations And Triangle Congruence-Truss Your Judgment

 11.1 Congruent Triangles Learning Targets p.144 11.2 Congruence Criteria Learning Targets p.147 11.3 Proving and Applying the Congruence Criteria Learning Targets p.154 11.4 Extending the Congruence Criteria Learning Targets p.160 Activity Practice p.165

### Chapter 12

Flowchart Proofs-Go With The Flow

 12.1 Flowchart Proofs Learning Targets p.168 12.2 Three Types of Proofs Learning Targets p.175 Activity Practice p.177

### Chapter 13

Properties Of Triangles-Best Two Out Of Three

 13.1 Angle Relationships in Triangles Learning Targets p.181 13.2 Isosceles Triangle Learning Targets p.186 Activity Practice p.189

### Chapter 14

Concurrent Segments In Triangles-What The Point?

 14.1 Altitudes of a Triangle Learning Targets p.192 14.2 Medians of a Triangle Learning Targets p.195 14.3 Perpendicular Bisectors and Angle Bisectors of a Triangle Learning Targets p.198 Activity Practice p.201

### Chapter 15

Quadrilaterals And Their Properties-A 4-Gon Hypothesis

 15.1 Kites and Triangle Midsegments Learning Targets p.205 15.2 Trapezoids Learning Targets p.209 15.3 Parallelograms Learning Targets p.213 15.4 Rectangles, Rhombuses, and Square Learning Targets p.216 Activity Practice p.221

### Chapter 16

 16.1 Proving a Quadrilateral is a Parallelogram Learning Targets p.223 16.2 Proving a Quadrilateral is a Rectangle Learning Targets p.227 16.3 Proving a Quadrilateral is a Rhombus Learning Targets p.230 16.4 Proving a Quadrilateral is a Square Learning Targets p.233 Activity Practice p.235

### Chapter 17

Dilations And Similarity Transformations-Scaling Up/Scaling Down

 17.1 Dilations Learning Targets p.241 17.2 Similarity Transformations Learning Targets p.248 17.3 Properties of Similar Figures Learning Targets p.252 Activity Practice p.255

### Chapter 18

Similar Triangles-Measuring Up

 18.1 Similarity Criteria Learning Targets p.257 18.2 Using Similarity Criteria Learning Targets p.262 18.3 Triangle Proportionality Learning Targets p.265 Activity Practice p.271

### Chapter 19

Geometric Mean-Do You Mean It?

 19.1 The Right Triangle Altitude Theorem Learning Targets p.275 19.2 The Geometric Mean Learning Targets p.278 Activity Practice p.281

### Chapter 20

The Pythagorean Theorem And Its Converse-Is That …

 20.1 Pythagorean Theorem Learning Targets p.283 20.2 Converse of the Pythagorean Theorem Learning Targets p.286 Activity Practice p.289

### Chapter 21

Special Right Triangles-The Community Quilting Project

 21.1 45° 45° 90° Triangles Learning Targets p.291 21.2 30° 60° 90° Triangles Learning Targets p.295 Activity Practice p.299

### Chapter 22

Basic Trigonometric Relationships-The Sine Of Things To …

 22.1 Similar Right Triangles Learning Targets p.303 22.2 Trigonometric Ratios Learning Targets p.308 22.3 Using Trigonometric Ratios Learning Targets p.312 22.4 Solving Right Triangles Learning Targets p.315 Activity Practice p.317

### Chapter 23

The Law Of Sines And Of Cosines-There …

 23.1 The Law of Sines Learning Targets p.319 23.2 The Ambiguous Case Learning Targets p.322 23.3 The Law of Cosines Learning Targets p.324 23.4 Solving Triangles Learning Targets p.327 Activity Practice p.329

### Chapter 24

Tangents And Chords-Off On A Tangent

 24.1 Circle Basics Learning Targets p.335 24.2 Theorems About Chords Learning Targets p.339 24.3 Tangent Segments Learning Targets p.345 Activity Practice p.347

### Chapter 25

Arcs And Angles-Coming Full Circle

 25.1 Arcs and Central Angles Learning Targets p.349 25.2 Inscribed Angles Learning Targets p.353 25.3 Angles Formed by Chords Learning Targets p.358 25.4 Angles Formed by Tangents and Secants Learning Targets p.363 Activity Practice p.369

### Chapter 26

Coordinate Proofs-Prove It!

 26.1 Proving the Midpoint Formula Learning Targets p.373 26.2 Proofs about Slope Learning Targets p.377 26.3 Proving Concurrency of Medians Learning Targets p.382 26.4 Points Along a Line Segment Learning Targets p.387 Activity Practice p.390

### Chapter 27

Equation Of A Circle-Round And Round

 27.1 Circles on the Coordinate Plane Learning Targets p.391 27.2 Completing the Square to Find the Center and Radius Learning Targets p.396 Activity Practice p.399

### Chapter 28

Equations Of Parabolas-Throwing A Curve

 28.1 Parabolas on the Coordinate Plane Learning Targets p.401 28.2 Parabolas with Vertex (h,k) Learning Targets p.405 Activity Practice p.409

### Chapter 29

Constructions-Constructive Thinking

 29.1 Constructions with Segments and Angles Learning Targets p.411 29.2 Constructions with Parallel and Perpendicular Lines Learning Targets p.418 29.3 Constructions with Circles Learning Targets p.422 Activity Practice p.427

### Chapter 30

Deriving Area Formulas-Shape Up

 30.1 Areas of Rectangles and Parallelograms Learning Targets p.433 30.2 Areas of Triangles Learning Targets p.437 30.3 Areasof Rhombuses and Trapezoids Learning Targets p.441 Activity Practice p.445

### Chapter 31

Regular Polygons-Plenty Of Polygons

 31.1 Sum of the Measures of the Interior Angles of a Polygons Learning Targets p.447 31.2 Regular Polygons and Exterior Angles Learning Targets p.453 31.3 Area and Perimeter of Regular Polygons Learning Targets p.457 Activity Practice p.461

### Chapter 32

Length And Area Of Circles-Pi In The …

 32.1 Circumference and Area of a Circle Learning Targets p.463 32.2 Sectors and Arcs Learning Targets p.467 32.3 Circles and Similarity Learning Targets p.470 Activity Practice p.475

### Chapter 33

 33.1 Prisms and Pyramids Learning Targets p.479 33.2 Cylinders and Cones Learning Targets p.486 33.3 Spheres and Solids of Rotation Learning Targets p.489 Activity Practice p.493

### Chapter 34

Prisms And Cylinders-Exterior Experiences

 34.1 Surface Area of Prisms and Cylinders Learning Targets p.495 34.2 Volume of Prisms and Cylinders Learning Targets p.500 Activity Practice p.505

### Chapter 35

Pyramids And Cones-Perfect Packaging

 35.1 Surface Area of Pyramids and Cones Learning Targets p.507 35.2 Volumes of Pyramids and Cones Learning Targets p.513 35.3 Density Learning Targets p.518 Activity Practice p.521

### Chapter 36

Spheres-Isn't That Spatial

 36.1 Surface Area of Spheres Learning Targets p.526 36.2 Volume of Spheres Learning Targets p.529 36.3 Spherical Geometry Learning Targets p.532 Activity Practice p.537

### Chapter 37

Changing Dimensions-Model Behavior

 37.1 Cubes and Spheres Learning Targets p.539 37.2 Pyramids and Cylinders Learning Targets p.542 Activity Practice p.547

### Chapter 38

Sample Spaces-Springboard Superstar And More

 38.1 Probability of a Single Event Learning Targets p.553 38.2 Events Involving "And" and "Or" Learning Targets p.559 Activity Practice p.565

### Chapter 39

Venn Diagrams And Probability Notation-Annabel Hs

 39.1 Using a Venn Diagram to Represent a Sample Space Learning Targets p.567 39.2 Using a Venn Diagram to Represent "And","Or", and "Not" Learning Targets p.573 Activity Practice p.579

### Chapter 40

Addition Rule And Mutually Exclusive Events-Hector St.

 40.1 Applying the Addition Rule Learning Targets p.581 40.2 Adapting the Addition Rule for Mutually Exclusive Events Learning Targets p.587 Activity Practice p.591

### Chapter 41

Dependent Events-Coco Wildlife Conservation Trust

 41.1 Understanding Conditional Probability Learning Targets p.595 41.2 The Conditional Probability Formula Learning Targets p.601 41.3 Tree Diagrams Learning Targets p.604 Activity Practice p.611

### Chapter 42

Independent Events-The Caribou, The Bear, And The …

 42.1 The Multiplaction Rule Learning Targets p.613 42.2 Geometric Probability Learning Targets p.621 42.3 Permutations and Combinations Learning Targets p.625 Activity Practice p.631

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