A TEXTBOOK OF GEOMETRY
Introduction 1 The Flashcard App 4 Definitions 5 The Basics 6 Bisectors and Midpoints 7 Types of Angles 13 Reflexive, Substitution, and Transitive Properties 19 Addition and Subtraction Postulates 20 Exercises 22 Triangle Proofs 27 Side-Side-Side Postulate for Proving Triangles Congruent 30 Side-Angle-Side Postulate for Proving Triangles Congruent 32 Angle-Side-Angle Postulate for Proving Triangles Congruent 34 Angle-Angle-Side Postulate for Proving Triangles Congruent 37 Why Is Side-Side-Angle Not a Postulate for Proving Triangles Congruent? 39 Why Is Angle-Angle-Angle Not a Postulate for Proving Triangles Congruent? 40 Hypotenuse-Leg Postulate for Proving Triangles Congruent 41 Corresponding Parts of Congruent Triangles Are Congruent 46 Exercises 50 Classifying Triangles 57 Solving for the Angles in a Triangle 58 Exterior Angle Theorem 59 Classifying Triangles by Angle Measurements 62 Isosceles, Equilateral, and Scalene Triangles 66 Relationships of the Sides and Angles of Triangles 73 Median, Altitude, and Angle Bisector 76 Exercises 87 Centers of a Triangle 93 Centroid of a Triangle 94 The Incenter of a Triangle 96 The Orthocenter of a Triangle 99 The Circumcenter of a Triangle 100 The Euler Line 104 Exercises 106 Similarity 109 Proportions in Similar Triangles 111 Determining Whether Triangles Are Similar 114 Perimeter and Area of Similar Triangles 116 Parallel Lines Inside a Triangle 118 Proportions of Similar Right Triangles 123 Similar Triangle Proofs 126 Exercises 132 Getting to Know Right Triangles 137 The Pythagorean Theorem 138 Pythagorean Triples 142 Special Right Triangles 142 Right Triangle Trigonometry 152 Word Problems 157 Exercises 161 Parallel Lines 165 Alternate Interior Angles 166 Corresponding Angles 169 Alternate Exterior, Same-Side Interior, and Same-Side Exterior Angles 172 Auxiliary Lines 176 Proving That the Sum of the Angles of a Triangle Is 180° 179 Determining If Lines Are Parallel 180 Exercises 186 Parallelograms 191 Rectangles 198 Rhombuses 200 Squares 202 Trapezoids 206 Median of a Trapezoid 209 Exercises 212 Coordinate Geometry 215 Distance Formula 218 Using the Distance Formula to Classify Shapes 219 Midpoint Formula 222 Slope Formula 225 Writing the Equations of Parallel and Perpendicular Lines 235 Partitioning a Line Segment 237 Exercises 242 Transformations 245 Reflections 246 Reflection Over the Y-Axis 246 Reflection Over the X-Axis 248 Reflection Over the Line y = x 248 Reflecting a Point Over Horizontal and Vertical Lines 249 Reflecting a Point Over an Oblique Line 252 Finding the Equation for the Line of Reflection 256 Point Reflections 258 Rotations 258 Summary of Rules for Rotations with the Center of Rotation at the Origin 259 Rotation with Center of Rotation Not at the Origin 260 Translations 262 Dilation 264 Dilations Not Centered at the Origin 268 Composition of Transformations 273 Exercises 277 Circle Theorems Involving Angles and Segments 281 Definition of Terms Related to a Circle 282 Lengths of Intersecting Chords 287 Finding the Length of Secant Segments 289 Length of Tangent–Secant Segments from an External Point 292 Angles Associated with the Circle 293 Central Angle 293 Inscribed Angle 294 Angle Formed by Two Intersecting Chords 296 Exterior Angles of a Circle 298 Exercises 300 Circumference and the Area of Circles 303 Finding the Area of a Sector 305 Finding the Length of the Arc of a Sector 309 Standard Form of a Circle 313 General Form of a Circle 314 Graphing a Circle on the Coordinate Plane 316 Exercises 320 Volume of Three-Dimensional Shapes 323 Cones 324 Cylinders 326 Prisms 329 Square Pyramids 334 Spheres 336 From 2D to 3D 337 Exercises 343 Constructions 347 Copying Segments and Angles 348 Bisectors and Perpendicular and Parallel Lines 351 Constructions Involving Perpendicular Lines 353 Constructing Parallel Lines 357 Construction Applications 359 Constructing an Altitude and a Median 365 Constructing a Square and Hexagon Inscribed in a Circle 367 Constructing Transformations 370 Exercises 381 Answer Key 385 Teacher’s Guide 477