GEOMETRY

1. Basic words for Geometry............................................... 11
1.1 Basic Words_ Points, Lines, and Planes................. 12
1.2 Basic Words_ Angles............................................ 15
1.3 Basic Words_ Special Pairs of Angles.................... 18
1.4 Basic Words_ Polygons........................................ 21
2. Geometric Reasoning...................................................... 25
2.1 Conditional Statements....................................... 26
2.2 Inverses and Contrapositives............................... 30
2.3 Postulates and Theorems..................................... 35
2.4 Writing Proofs..................................................... 41
2.5 Segments and Angle Relationships....................... 49
2.6 Special Pairs of Angles........................................ 58
2.7 Perpendicular Lines............................................. 67
2.8 Theorems about Special Pairs of Angles............... 72
Postulates or Theorems from Chapter 2..................... 78
3. Parallel Lines................................................................... 81
3.1 Parallel Lines and Transversals............................. 82
3.2 Angles and Parallel Lines..................................... 88
3.3 Proving Lines Parallel.......................................... 95
3.4 Angles of Triangles............................................ 104
Postulates or Theorems from Chapter 3................... 110
4. Congruent triangles....................................................... 115
4.1 Congruent Polygons.......................................... 116
4.2 Proving Congruence_ SSS, SAS, ASA................. 119
4.3 Proving Congruence_ AAS, HL........................... 126
4.4 CPCTC.............................................................. 132
4.5 Isosceles Triangles............................................. 139
4.6 Using Congruent Triangles................................ 147
Postulates or Theorems from Chapter 4................... 150

5. Relationships in Triangles..............................................153
5.1 Median, Altitude, and Bisectors.........................154
5.2 Centers of Triangles..........................................161
5.3 Midsegment Theorem........................................174
5.4 Properties of Inequalities...................................179
5.5 Inequalities in One Triangle................................186
5.6 Inequalities in Two Triangles..............................192
Postulates or Theorems from Chapter 5...................198
6. Quadrilaterals.................................................................201
6.1 Angles of Polygons............................................202
6.2 Parallelograms..................................................210
6.3 Tests for Parallelograms.....................................218
6.4 Rectangles, Rhombi and Squares.......................225
6.5 Trapezoids........................................................238
Postulates or Theorems from Chapter 6...................247
7. Similarity........................................................................251
7.1 Proportions.......................................................252
7.2 Identify Similar Figures......................................257
7.3 Proving Similar Triangles...................................261
7.4 More Theorems about Similar Triangles..............275
Postulates or Theorems from Chapter 7...................283
8. Right Triangles and Trigonometry..................................285
8.1 Right Triangle Similarity....................................286
8.2 The Pythagorean Theorem 291
8.3 Special Right Triangles......................................299
8.4 Trigonometry of Right Triangles.........................305
8.5 Angle of elevation or depression........................311

9. Circles............................................................................ 317
9.1 Basic words _Circles and Arcs............................ 318
9.2 Tangent Lines................................................... 322
9.3 Common Tangents and Tangent Circles.............. 333
9.4 Chords and Arcs................................................ 341
9.5 Inscribed Angles................................................ 355
9.6 Secants, Tangents, and Angle Measures............. 373
9.7 Secants, Tangents, and Segments...................... 382
Postulates or Theorems from Chapter 9................... 390
10. Areas of Plane Figures ................................................ 393
10.1 Area of polygons............................................. 394
10.2 Area of regular polygons................................. 402
10.3 Area of Circles and Sectors.............................. 408
10.4 Areas and Ratios............................................. 419
11. Areas and Volumes of Solids....................................... 429
11.1 Basic words _3D Solid...................................... 430
11.2 Surface Area.................................................. 435
11.3 Volume........................................................... 443
11.4 Sphere............................................................ 456
11.5 Area and Volume of similar Solids.................... 464
12. Coordinate Geometry.................................................. 473
12.1 Transformation............................................... 474
12.2 Distance and Midpoints................................... 482
12.3 Equation of Circle........................................... 486
12.4 Slope of a Line................................................ 493
12.5 Coordinate Geometry Proofs........................... 498
Abbreviations..................................................................... 507
Answers............................................................................. 509